big rearrangement of files to make libraries and example (research) files clearer, and changed to c++ std lib random numbers

28 files changed, 2637 insertions, 0 deletions

diff --git a/examples/CMakeLists.txt b/examples/CMakeLists.txt
new file mode 100644
index 0000000..baf0a10
--- /dev/null
+++ b/examples/CMakeLists.txt
@@ -0,0 +1,7 @@
+
+add_library(wolff_examples INTERFACE)
+
+target_include_directories(wolff_examples INTERFACE include)
+
+add_subdirectory(src)
+
diff --git a/examples/include/colors.h b/examples/include/colors.h
new file mode 100644
index 0000000..abf137c
--- /dev/null
+++ b/examples/include/colors.h
@@ -0,0 +1,34 @@
+#pragma once
+
+#include <wolff/types.h>
+
+double hue_to_R(double theta) {
+  if (((M_PI / 3 <= theta) && (theta < 2 * M_PI / 3)) || ((4 * M_PI / 3 <= theta) && (theta < 5 * M_PI / 3))) {
+    return 1.0 - fabs(fmod(theta / (2 * M_PI / 6), 2) - 1.0);
+  } else if (((0 <= theta) && (theta < M_PI / 3)) || ((5 * M_PI / 3 <= theta) && (theta <= 2 * M_PI))) {
+    return 1.0;
+  } else {
+    return 0.0;
+  }
+}
+
+double hue_to_G(double theta) {
+  if (((0 <= theta) && (theta < M_PI / 3)) || ((M_PI <= theta) && (theta < 4 * M_PI / 3))) {
+    return 1.0 - fabs(fmod(theta / (2 * M_PI / 6), 2) - 1.0);
+  } else if (((M_PI / 3 <= theta) && (theta < 2 * M_PI / 3)) || ((2 * M_PI / 3 <= theta) && (theta < M_PI))) {
+    return 1.0;
+  } else {
+    return 0.0;
+  }
+}
+
+double hue_to_B(double theta) {
+  if (((2 * M_PI / 3 <= theta) && (theta < M_PI)) || ((5 * M_PI / 3 <= theta) && (theta <= 2 * M_PI))) {
+    return 1.0 - fabs(fmod(theta / (2 * M_PI / 6), 2) - 1.0);
+  } else if (((M_PI <= theta) && (theta < 4 * M_PI / 3)) || ((4 * M_PI / 3 <= theta) && (theta < 5 * M_PI / 3))) {
+    return 1.0;
+  } else {
+    return 0.0;
+  }
+}
+
diff --git a/examples/include/correlation.hpp b/examples/include/correlation.hpp
new file mode 100644
index 0000000..042cff3
--- /dev/null
+++ b/examples/include/correlation.hpp
@@ -0,0 +1,23 @@
+
+#pragma once
+
+#include <wolff/types.h>
+#include <wolff/state.hpp>
+
+#include <fftw3.h>
+
+template <class R_t, class X_t>
+double correlation_length(const state_t <R_t, X_t>& s) {
+  double total = 0;
+
+#ifdef DIMENSION
+  for (D_t j = 0; j < DIMENSION; j++) {
+#else
+  for (D_t j = 0; j < s.D; j++) {
+#endif
+    total += norm_squared(s.ReF[j]) + norm_squared(s.ImF[j]);
+  }
+
+  return total / s.D;
+}
+
diff --git a/examples/include/measure.hpp b/examples/include/measure.hpp
new file mode 100644
index 0000000..e20353c
--- /dev/null
+++ b/examples/include/measure.hpp
@@ -0,0 +1,63 @@
+
+#pragma once
+
+#include <wolff/state.hpp>
+#include "correlation.hpp"
+#include <functional>
+
+#define POSSIBLE_MEASUREMENTS 4
+const unsigned char measurement_energy        = 1 << 0;
+const unsigned char measurement_clusterSize   = 1 << 1;
+const unsigned char measurement_magnetization = 1 << 2;
+const unsigned char measurement_fourierZero    = 1 << 3;
+
+char const *measurement_labels[] = {"E", "S", "M", "F"};
+
+FILE **measure_setup_files(unsigned char flags, unsigned long timestamp) {
+  FILE **files = (FILE **)calloc(POSSIBLE_MEASUREMENTS, sizeof(FILE *));
+
+  for (uint8_t i = 0; i < POSSIBLE_MEASUREMENTS; i++) {
+    if (flags & (1 << i)) {
+      char *filename = (char *)malloc(255 * sizeof(char));
+      sprintf(filename, "wolff_%lu_%s.dat", timestamp, measurement_labels[i]);
+      files[i] = fopen(filename, "wb");
+      free(filename);
+    }
+  }
+
+  return files;
+}
+
+template <class R_t, class X_t>
+std::function <void(const state_t <R_t, X_t>&)> measure_function_write_files(unsigned char flags, FILE **files, std::function <void(const state_t <R_t, X_t>&)> other_f) {
+  return [=] (const state_t <R_t, X_t>& s) {
+    if (flags & measurement_energy) {
+      float smaller_E = (float)s.E;
+      fwrite(&smaller_E, sizeof(float), 1, files[0]);
+    }
+    if (flags & measurement_clusterSize) {
+      fwrite(&(s.last_cluster_size), sizeof(uint32_t), 1, files[1]);
+    }
+    if (flags & measurement_magnetization) {
+      write_magnetization(s.M, files[2]);
+    }
+    if (flags & measurement_fourierZero) {
+      float smaller_X = (float)correlation_length(s);
+      fwrite(&smaller_X, sizeof(float), 1, files[3]);
+    }
+
+    other_f(s);
+  };
+}
+
+void measure_free_files(unsigned char flags, FILE **files) {
+  for (uint8_t i = 0; i < POSSIBLE_MEASUREMENTS; i++) {
+    if (flags & (1 << i)) {
+      fclose(files[i]);
+    }
+  }
+
+  free(files);
+}
+
+
diff --git a/examples/include/randutils b/examples/include/randutils
new file mode 160000
+Subproject 8486a610a954a8248c12485fb4cfc390a5f5f85
diff --git a/examples/src/CMakeLists.txt b/examples/src/CMakeLists.txt
new file mode 100644
index 0000000..3397426
--- /dev/null
+++ b/examples/src/CMakeLists.txt
@@ -0,0 +1,4 @@
+
+add_subdirectory(models)
+add_subdirectory(tools)
+
diff --git a/examples/src/models/CMakeLists.txt b/examples/src/models/CMakeLists.txt
new file mode 100644
index 0000000..0b0c111
--- /dev/null
+++ b/examples/src/models/CMakeLists.txt
@@ -0,0 +1,6 @@
+
+add_subdirectory(ising)
+add_subdirectory(On)
+add_subdirectory(potts)
+add_subdirectory(roughening)
+
diff --git a/examples/src/models/On/CMakeLists.txt b/examples/src/models/On/CMakeLists.txt
new file mode 100644
index 0000000..26985b9
--- /dev/null
+++ b/examples/src/models/On/CMakeLists.txt
@@ -0,0 +1,29 @@
+
+add_executable(wolff_planar               wolff_On.cpp)
+add_executable(wolff_planar_2d_no-field   wolff_On.cpp)
+add_executable(wolff_heisenberg           wolff_On.cpp)
+
+set_target_properties(wolff_planar             PROPERTIES COMPILE_FLAGS "-DN_COMP=2")
+set_target_properties(wolff_planar_2d_no-field PROPERTIES COMPILE_FLAGS "-DN_COMP=2 -DDIMENSION=2 -DNOFIELD")
+set_target_properties(wolff_heisenberg         PROPERTIES COMPILE_FLAGS "-DN_COMP=3")
+
+find_library(GL NAMES GL)
+find_library(GLU NAMES GLU)
+find_library(GLUT NAMES glut)
+
+if (${GLUT} MATCHES "GLUT-NOTFOUND")
+  target_link_libraries(wolff_planar             wolff wolff_examples)
+  target_link_libraries(wolff_planar_2d_no-field wolff wolff_examples)
+  target_link_libraries(wolff_heisenberg         wolff wolff_examples)
+else()
+  target_compile_definitions(wolff_planar             PUBLIC HAVE_GLUT)
+  target_compile_definitions(wolff_planar_2d_no-field             PUBLIC HAVE_GLUT)
+  target_compile_definitions(wolff_heisenberg             PUBLIC HAVE_GLUT)
+
+  target_link_libraries(wolff_planar             wolff wolff_examples glut GL GLU)
+  target_link_libraries(wolff_planar_2d_no-field wolff wolff_examples glut GL GLU)
+  target_link_libraries(wolff_heisenberg             wolff wolff_examples glut GL GLU)
+endif()
+
+install(TARGETS wolff_planar wolff_planar_2d_no-field wolff_heisenberg DESTINATION ${CMAKE_INSTALL_BINDIR})
+
diff --git a/examples/src/models/On/orthogonal.hpp b/examples/src/models/On/orthogonal.hpp
new file mode 100644
index 0000000..f13357f
--- /dev/null
+++ b/examples/src/models/On/orthogonal.hpp
@@ -0,0 +1,202 @@
+
+#pragma once
+
+#include <stdlib.h>
+#include <random>
+#include <cmath>
+
+#include <wolff/state.hpp>
+#include <wolff/types.h>
+#include "vector.hpp"
+
+template <q_t q, class T>
+class orthogonal_t : public std::array<std::array<T, q>, q> {
+  public :
+  bool is_reflection;
+
+  orthogonal_t() : is_reflection(false) {
+    for (q_t i = 0; i < q; i++) {
+      (*this)[i].fill(0);
+      (*this)[i][i] = (T)1;
+    }
+  }
+
+  vector_t<q, T> act(const vector_t <q, T>& v) const {
+    vector_t <q, T> v_rot;
+    v_rot.fill(0);
+
+    if (is_reflection) {
+      double prod = 0;
+      for (q_t i = 0; i < q; i++) {
+        prod += v[i] * (*this)[0][i];
+      }
+      for (q_t i = 0; i < q; i++) {
+        v_rot[i] = v[i] - 2 * prod * (*this)[0][i];
+      }
+    } else {
+      for (q_t i = 0; i < q; i++) {
+        for (q_t j = 0; j < q; j++) {
+          v_rot[i] += (*this)[i][j] * v[j];
+        }
+      }
+    }
+
+    return v_rot;
+  }
+
+  orthogonal_t<q, T> act(const orthogonal_t <q, T>& m) const {
+    orthogonal_t <q, T> m_rot;
+
+    m_rot.is_reflection = false;
+
+    if (is_reflection) {
+      for (q_t i = 0; i < q; i++) {
+        double akOki = 0;
+
+        for (q_t k = 0; k < q; k++) {
+          akOki += (*this)[0][k] * m[k][i];
+        }
+
+        for (q_t j = 0; j < q; j++) {
+          m_rot[j][i] = m[j][i] - 2 * akOki * (*this)[0][j];
+        }
+      }
+    } else {
+      for (q_t i = 0; i < q; i++) {
+        m_rot[i].fill(0);
+        for (q_t j = 0; j < q; j++) {
+          for (q_t k = 0; k < q; k++) {
+            m_rot[i][j] += (*this)[i][j] * m[j][k];
+          }
+        }
+      }
+    }
+
+    return m_rot;
+  }
+
+  vector_t <q, T> act_inverse(const vector_t <q, T>& v) const {
+    if (is_reflection) {
+      return this->act(v); // reflections are their own inverse
+    } else {
+      vector_t <q, T> v_rot;
+      v_rot.fill(0);
+
+      for (q_t i = 0; i < q; i++) {
+        for (q_t j = 0; j < q; j++) {
+          v_rot[i] += (*this)[j][i] * v[j];
+        }
+      }
+
+      return v_rot;
+    }
+  }
+
+  vector_t <q, T> act_inverse(const orthogonal_t <q, T>& m) const {
+    if (is_reflection) {
+      return this->act(m); // reflections are their own inverse
+    } else {
+      orthogonal_t <q, T> m_rot;
+      m_rot.is_reflection = false;
+
+      for (q_t i = 0; i < q; i++) {
+        m_rot[i].fill(0);
+        for (q_t j = 0; j < q; j++) {
+          for (q_t k = 0; k < q; k++) {
+            m_rot[i][j] += (*this)[j][i] * m[j][k];
+          }
+        }
+      }
+
+      return m_rot;
+    }
+  }
+
+};
+
+
+template <q_t q>
+orthogonal_t <q, double> generate_rotation_uniform (std::mt19937& r, const vector_t <q, double>& v) {
+  std::normal_distribution<double> dist(0.0,1.0);
+  orthogonal_t <q, double> ptr;
+  ptr.is_reflection = true;
+
+  double v2 = 0;
+
+  for (q_t i = 0; i < q; i++) {
+    ptr[0][i] = dist(r);
+    v2 += ptr[0][i] * ptr[0][i];
+  }
+
+  double mag_v = sqrt(v2);
+
+  for (q_t i = 0; i < q; i++) {
+    ptr[0][i] /= mag_v;
+  }
+
+  return ptr;
+}
+
+template <q_t q>
+orthogonal_t <q, double> generate_rotation_perturbation (std::mt19937& r, const vector_t <q, double>& v0, double epsilon, unsigned int n) {
+  std::normal_distribution<double> dist(0.0,1.0);
+  orthogonal_t <q, double> m;
+  m.is_reflection = true;
+
+  vector_t <q, double> v;
+
+  if (n > 1) {
+    std::uniform_int_distribution<unsigned int> udist(0, n);
+    unsigned int rotation = udist(r);
+
+    double cosr = cos(2 * M_PI * rotation / (double)n / 2.0);
+    double sinr = sin(2 * M_PI * rotation / (double)n / 2.0);
+
+    v[0] = v0[0] * cosr - v0[1] * sinr;
+    v[1] = v0[1] * cosr + v0[0] * sinr;
+
+    for (q_t i = 2; i < q; i++) {
+      v[i] = v0[i];
+    }
+  } else {
+    v = v0;
+  }
+
+  double m_dot_v = 0;
+
+  for (q_t i = 0; i < q; i++) {
+    m[0][i] = dist(r); // create a random vector
+    m_dot_v += m[0][i] * v[i];
+  }
+
+  double v2 = 0;
+
+  for (q_t i = 0; i < q; i++) {
+    m[0][i] = m[0][i] - m_dot_v * v[i]; // find the component orthogonal to v
+    v2 += pow(m[0][i], 2);
+  }
+
+  double mag_v = sqrt(v2);
+
+  for (q_t i = 0; i < q; i++) {
+    m[0][i] /= mag_v; // normalize
+  }
+
+  v2 = 0;
+
+  double factor = epsilon * dist(r);
+
+  for (q_t i = 0; i < q; i++) {
+    m[0][i] += factor * v[i]; // perturb orthogonal vector in original direction
+    v2 += pow(m[0][i], 2);
+  }
+
+  mag_v = sqrt(v2);
+
+  for (q_t i = 0; i < q; i++) {
+    m[0][i] /= mag_v; // normalize
+  }
+
+  return m;
+}
+
diff --git a/examples/src/models/On/vector.hpp b/examples/src/models/On/vector.hpp
new file mode 100644
index 0000000..1cdb60a
--- /dev/null
+++ b/examples/src/models/On/vector.hpp
@@ -0,0 +1,118 @@
+
+#pragma once
+
+#include <stdlib.h>
+#include <cmath>
+#include <array>
+
+#include <wolff/types.h>
+
+template <q_t q, class T>
+class vector_t : public std::array<T, q> {
+  public: 
+
+    // M_t needs to hold the sum of nv spins
+    typedef vector_t <q, T> M_t;
+
+    // F_t needs to hold the double-weighted sum of spins
+    typedef vector_t <q, double> F_t;
+
+    vector_t() {
+      this->fill((T)0);
+      (*this)[1] = (T)1;
+    }
+
+    vector_t(const T *x) {
+      for (q_t i = 0; i < q; i++) {
+        (*this)[i] = x[i];
+      }
+    }
+
+    template <class U>
+    inline vector_t<q, T>& operator+=(const vector_t<q, U> &v) {
+      for (q_t i = 0; i < q; i++) {
+        (*this)[i] += (U)v[i];
+      }
+      return *this;
+    }
+
+    template <class U>
+    inline vector_t<q, T>& operator-=(const vector_t<q, U> &v) {
+      for (q_t i = 0; i < q; i++) {
+        (*this)[i] -= (U)v[i];
+      }
+      return *this;
+    }
+
+    inline vector_t<q, T> operator*(v_t x) const {
+      vector_t<q, T> result;
+      for (q_t i = 0; i < q; i++) {
+        result[i] = x * (*this)[i];
+      }
+
+      return result;
+    }
+
+    inline vector_t<q, double> operator*(double x) const {
+      vector_t<q, double> result;
+      for (q_t i = 0; i < q; i++) {
+        result[i] = x * (*this)[i];
+      }
+
+      return result;
+    }
+
+    inline vector_t<q, T> operator-(const vector_t<q, T>& v) const {
+      vector_t<q, T> diff = *this;
+      diff -= v;
+      return diff;
+    }
+};
+
+
+template<q_t q, class T>
+double norm_squared(vector_t<q, T> v) {
+  double tmp = 0;
+  for (T &x : v) {
+    tmp += pow(x, 2);
+  }
+
+  return tmp;
+}
+
+template <q_t q, class T>
+void write_magnetization(vector_t <q, T> M, FILE *outfile) {
+  for (q_t i = 0; i < q; i++) {
+    fwrite(&(M[i]), sizeof(T), q, outfile);
+  }
+}
+
+// below functions and definitions are unnecessary for wolff.h but useful.
+
+template <q_t q> // save some space and don't write whole doubles
+void write_magnetization(vector_t <q, double> M, FILE *outfile) {
+  for (q_t i = 0; i < q; i++) {
+    float M_tmp = (float)M[i];
+    fwrite(&M_tmp, sizeof(float), 1, outfile);
+  }
+}
+
+template <q_t q, class T>
+T dot(const vector_t <q, T>& v1, const vector_t <q, T>& v2) {
+  T prod = 0;
+
+  for (q_t i = 0; i < q; i++) {
+    prod += v1[i] * v2[i];
+  }
+
+  return prod;
+}
+
+template <q_t q, class T>
+double H_vector(const vector_t <q, T>& v1, T *H) {
+  vector_t <q, T> H_vec(H);
+  return (double)(dot <q, T> (v1, H_vec));
+}
+
+char const *ON_strings[] = {"TRIVIAL", "ISING", "PLANAR", "HEISENBERG"};
+
diff --git a/examples/src/models/On/wolff_On.cpp b/examples/src/models/On/wolff_On.cpp
new file mode 100644
index 0000000..e3568c7
--- /dev/null
+++ b/examples/src/models/On/wolff_On.cpp
@@ -0,0 +1,268 @@
+
+#include <getopt.h>
+#include <stdio.h>
+
+#ifdef HAVE_GLUT
+#include <GL/glut.h>
+#endif
+
+#include "orthogonal.hpp"
+#include "vector.hpp"
+
+#include <wolff.hpp>
+#include <measure.hpp>
+#include <colors.h>
+#include <randutils/randutils.hpp>
+
+typedef orthogonal_t <N_COMP, double> orthogonal_R_t;
+typedef vector_t <N_COMP, double> vector_R_t;
+typedef state_t <orthogonal_R_t, vector_R_t> On_t;
+
+// angle from the x-axis of a two-vector
+double theta(vector_R_t v) {
+  double x = v[0];
+  double y = v[1];
+
+  double val = atan(y / x);
+
+  if (x < 0.0 && y > 0.0) {
+    return M_PI + val;
+  } else if ( x < 0.0 && y < 0.0 ) {
+    return - M_PI + val;
+  } else {
+    return val;
+  }
+}
+
+double H_modulated(vector_R_t v, int order, double mag) {
+  return mag * cos(order * theta(v));
+}
+
+int main(int argc, char *argv[]) {
+
+  count_t N = (count_t)1e7;
+
+#ifdef DIMENSION
+  D_t D = DIMENSION;
+#else
+  D_t D = 2;
+#endif
+  L_t L = 128;
+  double T = 2.26918531421;
+  double *H_vec = (double *)calloc(MAX_Q, sizeof(double));
+
+  bool silent = false;
+  bool use_pert = false;
+  bool N_is_sweeps = false;
+  bool draw = false;
+  unsigned int window_size = 512;
+
+  bool modulated_field = false;
+  unsigned int order = 1;
+
+  int opt;
+  q_t H_ind = 0;
+  double epsilon = 1;
+
+//  unsigned char measurement_flags = measurement_energy | measurement_clusterSize;
+
+  unsigned char measurement_flags = 0;
+
+  while ((opt = getopt(argc, argv, "N:D:L:T:H:spe:mo:M:Sdw:")) != -1) {
+    switch (opt) {
+    case 'N': // number of steps
+      N = (count_t)atof(optarg);
+      break;
+#ifdef DIMENSION
+    case 'D': // dimension
+      printf("Dimension was specified at compile time, you can't change it now!\n");
+      exit(EXIT_FAILURE);
+#else
+    case 'D': // dimension
+      D = atoi(optarg);
+      break;
+#endif
+    case 'L': // linear size
+      L = atoi(optarg);
+      break;
+    case 'T': // temperature 
+      T = atof(optarg);
+      break;
+    case 'H': // external field. nth call couples to state n
+      H_vec[H_ind] = atof(optarg);
+      H_ind++;
+      break;
+    case 's': // don't print anything during simulation. speeds up slightly
+      silent = true;
+      break;
+    case 'p':
+      use_pert = true;
+      break;
+    case 'e':
+      epsilon = atof(optarg);
+      break;
+    case 'm':
+      modulated_field = true;
+      break;
+    case 'M':
+      measurement_flags ^= 1 << atoi(optarg);
+      break;
+    case 'o':
+      order = atoi(optarg);
+      break;
+    case 'S':
+      N_is_sweeps = true;
+      break;
+    case 'd':
+#ifdef HAVE_GLUT
+      draw = true;
+      break;
+#else
+      printf("You didn't compile this with the glut library installed!\n");
+      exit(EXIT_FAILURE);
+#endif
+    case 'w':
+      window_size = atoi(optarg);
+      break;
+    default:
+      exit(EXIT_FAILURE);
+    }
+  }
+
+  unsigned long timestamp;
+
+  {
+    struct timespec spec;
+    clock_gettime(CLOCK_REALTIME, &spec);
+    timestamp = spec.tv_sec*1000000000LL + spec.tv_nsec;
+  }
+
+  const char *pert_type;
+
+  std::function <orthogonal_R_t(std::mt19937&, vector_R_t)> gen_R;
+
+  if (use_pert) {
+    double Hish;
+    if (modulated_field) {
+      Hish = fabs(H_vec[0]);
+    } else {
+      double H2 = 0;
+      for (q_t i = 0; i < N_COMP; i++) {
+        H2 += pow(H_vec[i], 2);
+      }
+      Hish = sqrt(H2);
+    }
+
+    epsilon = sqrt((N_COMP - 1) * T / (D + Hish / 2)) / 2;
+
+    gen_R = std::bind(generate_rotation_perturbation <N_COMP>, std::placeholders::_1, std::placeholders::_2, epsilon, order);
+    pert_type = "PERTURB5";
+  } else {
+    gen_R = generate_rotation_uniform <N_COMP>;
+    pert_type = "UNIFORM";
+  }
+
+  FILE *outfile_info = fopen("wolff_metadata.txt", "a");
+
+  fprintf(outfile_info, "<| \"ID\" -> %lu, \"MODEL\" -> \"%s\", \"q\" -> %d, \"D\" -> %" PRID ", \"L\" -> %" PRIL ", \"NV\" -> %" PRIv ", \"NE\" -> %" PRIv ", \"T\" -> %.15f, \"FIELD_TYPE\" -> ", timestamp, ON_strings[N_COMP], N_COMP, D, L, (v_t)pow(L, D), D * (v_t)pow(L, D), T);
+  if (modulated_field) {
+    fprintf(outfile_info, "\"MODULATED\", \"ORDER\" -> %d, \"H\" -> %.15f, ", order, H_vec[0]);
+  } else {
+    fprintf(outfile_info, "\"VECTOR\", \"H\" -> {");
+    for (q_t i = 0; i < N_COMP; i++) {
+      fprintf(outfile_info, "%.15f", H_vec[i]);
+      if (i < N_COMP - 1) {
+        fprintf(outfile_info, ", ");
+      }
+    }
+    fprintf(outfile_info, "}, ");
+  }
+
+  fprintf(outfile_info, "\"GENERATOR\" -> \"%s\"", pert_type);
+
+  if (use_pert) {
+    fprintf(outfile_info, ", \"EPS\" -> %g", epsilon);
+  }
+
+  fprintf(outfile_info, " |>\n");
+
+  fclose(outfile_info);
+
+  FILE **outfiles = measure_setup_files(measurement_flags, timestamp);
+
+  std::function <void(const On_t&)> other_f;
+  uint64_t sum_of_clusterSize = 0;
+
+  if (N_is_sweeps) {
+    other_f = [&] (const On_t& s) {
+      sum_of_clusterSize += s.last_cluster_size;
+    };
+  } else if (draw) {
+#ifdef HAVE_GLUT
+    // initialize glut
+    glutInit(&argc, argv);
+    glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB);
+    glutInitWindowSize(window_size, window_size);
+    glutCreateWindow("wolff");
+    glClearColor(0.0,0.0,0.0,0.0);
+    glMatrixMode(GL_PROJECTION);
+    glLoadIdentity();
+    gluOrtho2D(0.0, L, 0.0, L);
+
+    other_f = [&] (const On_t& s) {
+      glClear(GL_COLOR_BUFFER_BIT);
+      for (v_t i = 0; i < pow(L, 2); i++) {
+        vector_R_t v_tmp = s.R.act_inverse(s.spins[i]);
+        double thetai = fmod(2 * M_PI + theta(v_tmp), 2 * M_PI);
+        double saturation = 0.7;
+        double value = 0.9;
+        double chroma = saturation * value;
+        glColor3f(chroma * hue_to_R(thetai) + (value - chroma), chroma * hue_to_G(thetai) + (value - chroma), chroma * hue_to_B(thetai) + (value - chroma));
+        glRecti(i / L, i % L, (i / L) + 1, (i % L) + 1);
+      }
+      glFlush();
+    };
+#endif
+  } else {
+    other_f = [] (const On_t& s) {};
+  }
+
+  std::function <void(const On_t&)> measurements = measure_function_write_files(measurement_flags, outfiles, other_f);
+
+  std::function <double(const vector_R_t&)> H;
+
+  if (modulated_field) {
+    H = std::bind(H_modulated, std::placeholders::_1, order, H_vec[0]);
+  } else {
+    H = std::bind(H_vector <N_COMP, double>, std::placeholders::_1, H_vec);
+  }
+
+  // initialize random number generator
+  randutils::auto_seed_128 seeds;
+  std::mt19937 rng{seeds};
+
+#ifndef NOFIELD
+  state_t <orthogonal_R_t, vector_R_t> s(D, L, T, dot <N_COMP, double>, H);
+#else
+  state_t <orthogonal_R_t, vector_R_t> s(D, L, T, dot <N_COMP, double>);
+#endif
+
+  if (N_is_sweeps) {
+    count_t N_rounds = 0;
+    printf("\n");
+    while (sum_of_clusterSize < N * s.nv) {
+      printf("\033[F\033[J\033[F\033[JWOLFF: sweep %" PRIu64 " / %" PRIu64 ": E = %.2f, S = %" PRIv "\n", (count_t)((double)sum_of_clusterSize / (double)s.nv), N, s.E, s.last_cluster_size);
+      wolff <orthogonal_R_t, vector_R_t> (N, s, gen_R, measurements, rng, silent);
+      N_rounds++;
+    }
+    printf("\033[F\033[J\033[F\033[JWOLFF: sweep %" PRIu64 " / %" PRIu64 ": E = %.2f, S = %" PRIv "\n\n", (count_t)((double)sum_of_clusterSize / (double)s.nv), N, s.E, s.last_cluster_size);
+  } else {
+    wolff <orthogonal_R_t, vector_R_t> (N, s, gen_R, measurements, rng, silent);
+  }
+
+  measure_free_files(measurement_flags, outfiles);
+  free(H_vec);
+
+  return 0;
+}
+
diff --git a/examples/src/models/ising/CMakeLists.txt b/examples/src/models/ising/CMakeLists.txt
new file mode 100644
index 0000000..e8fbc9a
--- /dev/null
+++ b/examples/src/models/ising/CMakeLists.txt
@@ -0,0 +1,28 @@
+
+add_executable(wolff_ising             wolff_ising.cpp)
+add_executable(wolff_ising_2d          wolff_ising.cpp)
+add_executable(wolff_ising_2d_no-field wolff_ising.cpp)
+
+set_target_properties(wolff_ising_2d          PROPERTIES COMPILE_FLAGS "-DDIMENSION=2")
+set_target_properties(wolff_ising_2d_no-field PROPERTIES COMPILE_FLAGS "-DDIMENSION=2 -DNOFIELD")
+
+find_library(GL NAMES GL)
+find_library(GLU NAMES GLU)
+find_library(GLUT NAMES glut)
+
+if (${GLUT} MATCHES "GLUT-NOTFOUND")
+  target_link_libraries(wolff_ising             wolff wolff_examples)
+  target_link_libraries(wolff_ising_2d          wolff wolff_examples)
+  target_link_libraries(wolff_ising_2d_no-field wolff wolff_examples)
+else()
+  target_compile_definitions(wolff_ising             PUBLIC HAVE_GLUT)
+  target_compile_definitions(wolff_ising_2d          PUBLIC HAVE_GLUT)
+  target_compile_definitions(wolff_ising_2d_no-field PUBLIC HAVE_GLUT)
+
+  target_link_libraries(wolff_ising             wolff wolff_examples glut GL GLU)
+  target_link_libraries(wolff_ising_2d          wolff wolff_examples glut GL GLU)
+  target_link_libraries(wolff_ising_2d_no-field wolff wolff_examples glut GL GLU)
+endif()
+
+install(TARGETS wolff_ising wolff_ising_2d wolff_ising_2d_no-field DESTINATION ${CMAKE_INSTALL_BINDIR})
+
diff --git a/examples/src/models/ising/ising.hpp b/examples/src/models/ising/ising.hpp
new file mode 100644
index 0000000..ae20840
--- /dev/null
+++ b/examples/src/models/ising/ising.hpp
@@ -0,0 +1,59 @@
+#pragma once
+
+#include <cmath>
+#include <stdio.h>
+
+#include <wolff/types.h>
+
+class ising_t {
+  public:
+    bool x;
+
+    typedef int M_t;
+    typedef double F_t;
+
+    ising_t() : x(false) {}
+    ising_t(bool x) : x(x) {}
+    ising_t(int x) : x((bool)x) {}
+
+    inline int operator*(v_t a) const {
+      if (x) {
+        return -(int)a;
+      } else {
+        return (int)a;
+      }
+    }
+
+    inline double operator*(double a) const {
+      if (x) {
+        return -a;
+      } else {
+        return a;
+      }
+    }
+
+    inline int operator-(const ising_t &s) const {
+      if (x == s.x) {
+        return 0;
+      } else {
+        if (x) {
+          return -2;
+        } else {
+          return 2;
+        }
+      }
+    }
+};
+
+double norm_squared(double s) {
+  return pow(s, 2);
+}
+
+void write_magnetization(int M, FILE *outfile) {
+  fwrite(&M, sizeof(int), 1, outfile);
+}
+
+#define N_STATES 2
+const ising_t states[2] = {ising_t(0), ising_t(1)};
+q_t state_to_ind(ising_t state) { return (q_t)state.x; }
+
diff --git a/examples/src/models/ising/wolff_ising.cpp b/examples/src/models/ising/wolff_ising.cpp
new file mode 100644
index 0000000..5bdaa82
--- /dev/null
+++ b/examples/src/models/ising/wolff_ising.cpp
@@ -0,0 +1,198 @@
+
+#include <getopt.h>
+#include <stdio.h>
+
+// if you have GLUT installed, you can see graphics!
+#ifdef HAVE_GLUT
+#include <GL/glut.h>
+#endif
+
+// include your group and spin space
+#include "z2.hpp"
+#include "ising.hpp"
+
+// finite_states.h can be included for spin types that have special variables
+// defined, and it causes wolff execution to use precomputed bond probabilities
+#include <wolff/finite_states.hpp>
+
+#include <randutils/randutils.hpp>
+
+// measure.hpp contains useful functions for saving timeseries to files
+#include <measure.hpp>
+
+// include wolff.hpp
+#include <wolff.hpp>
+
+int main(int argc, char *argv[]) {
+
+  count_t N = (count_t)1e4;
+
+  D_t D = 2;
+  L_t L = 128;
+  double T = 2.26918531421;
+  double H = 0.0;
+
+  bool silent = false;
+  bool draw = false;
+  bool N_is_sweeps = false;
+  unsigned int window_size = 512;
+
+  // don't measure anything by default
+  unsigned char measurement_flags = 0;
+
+  int opt;
+
+  while ((opt = getopt(argc, argv, "N:D:L:T:H:sdw:M:S")) != -1) {
+    switch (opt) {
+    case 'N': // number of steps
+      N = (count_t)atof(optarg);
+      break;
+    case 'D': // dimension
+      D = atoi(optarg);
+      break;
+    case 'L': // linear size
+      L = atoi(optarg);
+      break;
+    case 'T': // temperature 
+      T = atof(optarg);
+      break;
+    case 'H': // external field
+      H = atof(optarg);
+      break;
+    case 's': // don't print anything during simulation. speeds up slightly
+      silent = true;
+      break;
+    case 'S':
+      N_is_sweeps = true;
+      break;
+    case 'd':
+#ifdef HAVE_GLUT
+      draw = true;
+      break;
+#else
+      printf("You didn't compile this with the glut library installed!\n");
+      exit(EXIT_FAILURE);
+#endif
+    case 'w':
+      window_size = atoi(optarg);
+      break;
+    case 'M':
+      measurement_flags ^= 1 << atoi(optarg);
+      break;
+    default:
+      exit(EXIT_FAILURE);
+    }
+  }
+
+  // get nanosecond timestamp for unique run id
+  unsigned long timestamp;
+
+  {
+    struct timespec spec;
+    clock_gettime(CLOCK_REALTIME, &spec);
+    timestamp = spec.tv_sec*1000000000LL + spec.tv_nsec;
+  }
+
+  // initialize random number generator
+  randutils::auto_seed_128 seeds;
+  std::mt19937 rng{seeds};
+
+  // define spin-spin coupling
+  std::function <double(const ising_t&, const ising_t&)> Z = [] (const ising_t& s1, const ising_t& s2) -> double {
+    if (s1.x == s2.x) {
+      return 1.0;
+    } else {
+      return -1.0;
+    }
+  };
+
+  // define spin-field coupling
+  std::function <double(const ising_t&)> B = [=] (const ising_t& s) -> double {
+    if (s.x) {
+      return -H;
+    } else {
+      return H;
+    }
+  };
+
+  // initialize state object
+#ifndef NOFIELD
+  state_t <z2_t, ising_t> s(D, L, T, Z, B);
+#else
+  state_t <z2_t, ising_t> s(D, L, T, Z);
+#endif
+
+  // define function that generates self-inverse rotations
+  std::function <z2_t(std::mt19937&, ising_t)> gen_R = [] (std::mt19937&, const ising_t& s) -> z2_t {
+    return z2_t(true);
+  };
+
+  FILE **outfiles = measure_setup_files(measurement_flags, timestamp);
+
+  std::function <void(const state_t<z2_t, ising_t>&)> other_f;
+  uint64_t sum_of_clusterSize = 0;
+
+  if (N_is_sweeps) {
+    other_f = [&] (const state_t<z2_t, ising_t>& s) {
+      sum_of_clusterSize += s.last_cluster_size;
+    };
+  } else if (draw) {
+#ifdef HAVE_GLUT
+    // initialize glut
+    glutInit(&argc, argv);
+    glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB);
+    glutInitWindowSize(window_size, window_size);
+    glutCreateWindow("wolff");
+    glClearColor(0.0,0.0,0.0,0.0);
+    glMatrixMode(GL_PROJECTION);
+    glLoadIdentity();
+    gluOrtho2D(0.0, L, 0.0, L);
+
+    other_f = [] (const state_t <z2_t, ising_t>& s) {
+      glClear(GL_COLOR_BUFFER_BIT);
+      for (v_t i = 0; i < pow(s.L, 2); i++) {
+        if (s.spins[i].x == s.R.x) {
+          glColor3f(0.0, 0.0, 0.0);
+        } else {
+          glColor3f(1.0, 1.0, 1.0);
+        }
+        glRecti(i / s.L, i % s.L, (i / s.L) + 1, (i % s.L) + 1);
+      }
+      glFlush();
+    };
+#endif
+  } else {
+    other_f = [] (const state_t<z2_t, ising_t>& s) {};
+  }
+
+  std::function <void(const state_t<z2_t, ising_t>&)> measurements = measure_function_write_files(measurement_flags, outfiles, other_f);
+
+  // add line to metadata file with run info
+  {
+    FILE *outfile_info = fopen("wolff_metadata.txt", "a");
+
+    fprintf(outfile_info, "<| \"ID\" -> %lu, \"MODEL\" -> \"ISING\", \"q\" -> 2, \"D\" -> %" PRID ", \"L\" -> %" PRIL ", \"NV\" -> %" PRIv ", \"NE\" -> %" PRIv ", \"T\" -> %.15f, \"H\" -> %.15f |>\n", timestamp, s.D, s.L, s.nv, s.ne, T, H);
+
+    fclose(outfile_info);
+  }
+
+  // run wolff for N cluster flips
+  if (N_is_sweeps) {
+    count_t N_rounds = 0;
+    printf("\n");
+    while (sum_of_clusterSize < N * s.nv) {
+      printf("\033[F\033[J\033[F\033[JWOLFF: sweep %" PRIu64 " / %" PRIu64 ": E = %.2f, S = %" PRIv "\n", (count_t)((double)sum_of_clusterSize / (double)s.nv), N, s.E, s.last_cluster_size);
+      wolff(N, s, gen_R, measurements, rng, silent);
+      N_rounds++;
+    }
+    printf("\033[F\033[J\033[F\033[JWOLFF: sweep %" PRIu64 " / %" PRIu64 ": E = %.2f, S = %" PRIv "\n\n", (count_t)((double)sum_of_clusterSize / (double)s.nv), N, s.E, s.last_cluster_size);
+  } else {
+    wolff(N, s, gen_R, measurements, rng, silent);
+  }
+
+  measure_free_files(measurement_flags, outfiles);
+
+  return 0;
+
+}
+
diff --git a/examples/src/models/ising/z2.hpp b/examples/src/models/ising/z2.hpp
new file mode 100644
index 0000000..19b6c05
--- /dev/null
+++ b/examples/src/models/ising/z2.hpp
@@ -0,0 +1,53 @@
+
+#pragma once
+
+#include <wolff/types.h>
+#include "ising.hpp"
+
+/* The minimum definition for a group type R_t to act on a spin type X_t is
+ * given by the following.
+ *
+ * void init(R_t *p);
+ * void free_spin(R_t r);
+ * R_t copy(R_t r);
+ * X_t act(R_t r, X_t x);
+ * R_t act(R_t r, R_t r);
+ * X_t act_inverse(R_t r, X_t x);
+ * R_t act_inverse(R_t r, R_t r);
+ *
+ */
+
+class z2_t {
+  public:
+  bool x;
+
+  z2_t() : x(false) {}
+
+  z2_t(bool x) : x(x) {}
+
+  ising_t act(const ising_t& s) const {
+    if (x) {
+      return ising_t(!s.x);
+    } else {
+      return ising_t(s.x);
+    }
+  }
+
+  z2_t act(const z2_t& r) const {
+    if (x) {
+      return z2_t(!r.x);
+    } else {
+      return z2_t(r.x);
+    }
+  }
+
+  ising_t act_inverse(const ising_t& s) const {
+    return this->act(s);
+  }
+
+  z2_t act_inverse(const z2_t& r) const {
+    return this->act(r);
+  }
+};
+
+
diff --git a/examples/src/models/potts/CMakeLists.txt b/examples/src/models/potts/CMakeLists.txt
new file mode 100644
index 0000000..53133b9
--- /dev/null
+++ b/examples/src/models/potts/CMakeLists.txt
@@ -0,0 +1,39 @@
+
+add_executable(wolff_3potts             wolff_potts.cpp)
+add_executable(wolff_4potts             wolff_potts.cpp)
+add_executable(wolff_7potts             wolff_potts.cpp)
+add_executable(wolff_3clock             wolff_clock.cpp)
+add_executable(wolff_5clock             wolff_clock.cpp)
+
+set_target_properties(wolff_3potts          PROPERTIES COMPILE_FLAGS "-DPOTTSQ=3")
+set_target_properties(wolff_4potts          PROPERTIES COMPILE_FLAGS "-DPOTTSQ=4")
+set_target_properties(wolff_7potts          PROPERTIES COMPILE_FLAGS "-DPOTTSQ=7")
+set_target_properties(wolff_3clock          PROPERTIES COMPILE_FLAGS "-DPOTTSQ=3")
+set_target_properties(wolff_5clock          PROPERTIES COMPILE_FLAGS "-DPOTTSQ=5")
+
+find_library(GL NAMES GL)
+find_library(GLU NAMES GLU)
+find_library(GLUT NAMES glut)
+
+if (${GLUT} MATCHES "GLUT-NOTFOUND")
+  target_link_libraries(wolff_3potts wolff wolff_examples)
+  target_link_libraries(wolff_4potts wolff wolff_examples)
+  target_link_libraries(wolff_7potts wolff wolff_examples)
+  target_link_libraries(wolff_3clock wolff wolff_examples)
+  target_link_libraries(wolff_5clock wolff wolff_examples)
+else()
+  target_compile_definitions(wolff_3potts PUBLIC HAVE_GLUT)
+  target_compile_definitions(wolff_4potts PUBLIC HAVE_GLUT)
+  target_compile_definitions(wolff_7potts PUBLIC HAVE_GLUT)
+  target_compile_definitions(wolff_3clock PUBLIC HAVE_GLUT)
+  target_compile_definitions(wolff_5clock PUBLIC HAVE_GLUT)
+
+  target_link_libraries(wolff_3potts             wolff wolff_examples glut GL GLU)
+  target_link_libraries(wolff_4potts             wolff wolff_examples glut GL GLU)
+  target_link_libraries(wolff_7potts             wolff wolff_examples glut GL GLU)
+  target_link_libraries(wolff_3clock             wolff wolff_examples glut GL GLU)
+  target_link_libraries(wolff_5clock             wolff wolff_examples glut GL GLU)
+endif()
+
+install(TARGETS wolff_3potts wolff_4potts wolff_7potts wolff_3clock wolff_5clock DESTINATION ${CMAKE_INSTALL_BINDIR})
+
diff --git a/examples/src/models/potts/dihedral.hpp b/examples/src/models/potts/dihedral.hpp
new file mode 100644
index 0000000..cbc5687
--- /dev/null
+++ b/examples/src/models/potts/dihedral.hpp
@@ -0,0 +1,48 @@
+
+#pragma once
+
+#include <wolff/types.h>
+#include "potts.hpp"
+
+template <q_t q>
+class dihedral_t {
+  public:
+    bool is_reflection;
+    q_t x;
+
+    dihedral_t() : is_reflection(false), x(0) {}
+    dihedral_t(bool x, q_t y) : is_reflection(x), x(y) {}
+
+    potts_t<q> act(const potts_t<q>& s) const {
+      if (this->is_reflection) {
+        return potts_t<q>(((q + this->x) - s.x) % q);
+      } else {
+        return potts_t<q>((this->x + s.x) % q);
+      }
+    }
+
+    dihedral_t<q> act(dihedral_t<q> r) const {
+      if (this->is_reflection) {
+        return dihedral_t<q>(!(r.is_reflection), ((q + this->x) - r.x) % q); 
+      } else {
+        return dihedral_t<q>(r.is_reflection, (this->x + r.x) % q);
+      }
+    }
+
+    potts_t<q> act_inverse(potts_t<q> s) const {
+      if (this->is_reflection) {
+        return this->act(s);
+      } else {
+        return potts_t<q>(((s.x + q) - this->x) % q);
+      }
+    }
+
+    dihedral_t<q> act_inverse(dihedral_t<q> r) const {
+      if (this->is_reflection) {
+        return this->act(r);
+      } else {
+        return dihedral_t<q>(r.is_reflection, ((r.x + q) - this->x) % q);
+      }
+    }
+};
+
diff --git a/examples/src/models/potts/potts.hpp b/examples/src/models/potts/potts.hpp
new file mode 100644
index 0000000..f4765e2
--- /dev/null
+++ b/examples/src/models/potts/potts.hpp
@@ -0,0 +1,72 @@
+#pragma once
+
+#include <cmath>
+#include <stdio.h>
+
+#include <wolff/types.h>
+#include "../On/vector.hpp"
+
+template <q_t q>
+class potts_t {
+  public:
+    q_t x;
+
+    typedef vector_t<q, int> M_t;
+    typedef vector_t<q, double> F_t;
+
+    potts_t() : x(0) {}
+    potts_t(q_t x) : x(x) {}
+
+    inline vector_t<q, int> operator*(v_t a) const {
+      vector_t<q, int> result;
+      result.fill(0);
+      result[x] = (int)a;
+
+      return result;
+    }
+
+    inline vector_t<q, double> operator*(double a) const {
+      vector_t<q, double> result;
+      result.fill(0.0);
+      result[x] = a;
+
+      return result;
+    }
+
+    inline vector_t<q, int> operator-(const potts_t<q> &s) const {
+      vector_t<q, int> result;
+      result.fill(0);
+
+      result[x]++;
+      result[s.x]--;
+
+      return result;
+    }
+};
+
+// we could inherit norm_squared from vector.h, but convention dictates that
+// potts norms be changed by a constant factor
+template <q_t q>
+double norm_squared(vector_t<q, double> s) {
+  double total = 0;
+  for (double& x : s) {
+    total += pow(x, 2);
+  }
+
+  return total * (double)q / ((double)q - 1.0);
+}
+
+// we could inherit write_magnetization from vector.h, but since M.x must sum
+// to nv we don't need to write the last element
+template <q_t q>
+void write_magnetization(vector_t<q, int> M, FILE *outfile) {
+  for (int& x : M) {
+    fwrite(&x, sizeof(int), q - 1, outfile);
+  }
+}
+
+// knock yourself out
+const potts_t<POTTSQ> states[256] = {{0}, {1}, {2}, {3}, {4}, {5}, {6}, {7}, {8}, {9}, {11}, {12}, {13}, {14}, {15}, {16}, {17}, {18}, {19}, {20}, {21}, {22}, {23}, {24}, {25}, {26}, {27}, {28}, {29}, {30}, {31}, {32}, {33}, {34}, {35}, {36}, {37}, {38}, {39}, {40}, {41}, {42}, {43}, {44}, {45}, {46}, {47}, {48}, {49}, {50}, {51}, {52}, {53}, {54}, {55}, {56}, {57}, {58}, {59}, {60}, {61}, {62}, {63}, {64}, {65}, {66}, {67}, {68}, {69}, {70}, {71}, {72}, {73}, {74}, {75}, {76}, {77}, {78}, {79}, {80}, {81}, {82}, {83}, {84}, {85}, {86}, {87}, {88}, {89}, {90}, {91}, {92}, {93}, {94}, {95}, {96}, {97}, {98}, {99}, {100}, {101}, {102}, {103}, {104}, {105}, {106}, {107}, {108}, {109}, {110}, {111}, {112}, {113}, {114}, {115}, {116}, {117}, {118}, {119}, {120}, {121}, {122}, {123}, {124}, {125}, {126}, {127}, {128}, {129}, {130}, {131}, {132}, {133}, {134}, {135}, {136}, {137}, {138}, {139}, {140}, {141}, {142}, {143}, {144}, {145}, {146}, {147}, {148}, {149}, {150}, {151}, {152}, {153}, {154}, {155}, {156}, {157}, {158}, {159}, {160}, {161}, {162}, {163}, {164}, {165}, {166}, {167}, {168}, {169}, {170}, {171}, {172}, {173}, {174}, {175}, {176}, {177}, {178}, {179}, {180}, {181}, {182}, {183}, {184}, {185}, {186}, {187}, {188}, {189}, {190}, {191}, {192}, {193}, {194}, {195}, {196}, {197}, {198}, {199}, {200}, {201}, {202}, {203}, {204}, {205}, {206}, {207}, {208}, {209}, {210}, {211}, {212}, {213}, {214}, {215}, {216}, {217}, {218}, {219}, {220}, {221}, {222}, {223}, {224}, {225}, {226}, {227}, {228}, {229}, {230}, {231}, {232}, {233}, {234}, {235}, {236}, {237}, {238}, {239}, {240}, {241}, {242}, {243}, {244}, {245}, {246}, {247}, {248}, {249}, {250}, {251}, {252}, {253}, {254}, {255}};
+template <q_t q>
+q_t state_to_ind(potts_t<q> state) { return (q_t)state.x; }
+
diff --git a/examples/src/models/potts/symmetric.hpp b/examples/src/models/potts/symmetric.hpp
new file mode 100644
index 0000000..8636f15
--- /dev/null
+++ b/examples/src/models/potts/symmetric.hpp
@@ -0,0 +1,51 @@
+
+#pragma once
+
+#include <stdlib.h>
+#include <array>
+#include <wolff/types.h>
+#include "potts.hpp"
+
+template <q_t q>
+class symmetric_t : public std::array<q_t, q> {
+  public:
+
+    symmetric_t() {
+      for (q_t i = 0; i < q; i++) {
+        (*this)[i] = i;
+      }
+    }
+
+    potts_t<q> act(const potts_t<q> &s) const {
+      return potts_t<q>((*this)[s.x]);
+    }
+
+    symmetric_t<q> act(const symmetric_t<q>& r) const {
+      symmetric_t<q> r_rot;
+      for (q_t i = 0; i < q; i++) {
+        r_rot[i] = (*this)[r[i]];
+      }
+
+      return r_rot;
+    }
+
+    potts_t<q> act_inverse(const potts_t<q>& s) const {
+      for (q_t i = 0; i < q; i++) {
+        if ((*this)[i] == s.x) {
+          return potts_t<q>(i);
+        }
+      }
+
+      exit(EXIT_FAILURE);
+    }
+
+    symmetric_t<q> act_inverse(const symmetric_t<q>& r) const {
+      symmetric_t<q> r_rot;
+      for (q_t i = 0; i < q; i++) {
+        r_rot[(*this)[i]] = r[i];
+      }
+
+      return r_rot;
+    }
+};
+
diff --git a/examples/src/models/potts/wolff_clock.cpp b/examples/src/models/potts/wolff_clock.cpp
new file mode 100644
index 0000000..020415d
--- /dev/null
+++ b/examples/src/models/potts/wolff_clock.cpp
@@ -0,0 +1,155 @@
+
+#include <getopt.h>
+
+#ifdef HAVE_GLUT
+#include <GL/glut.h>
+#endif
+
+// include your group and spin space
+#include "dihedral.hpp"
+#include "potts.hpp"
+#include <colors.h>
+
+// hack to speed things up considerably
+#define N_STATES POTTSQ
+#include <wolff/finite_states.hpp>
+
+#include <randutils/randutils.hpp>
+
+// include wolff.hpp
+#include <wolff.hpp>
+
+typedef state_t <dihedral_t<POTTSQ>, potts_t<POTTSQ>> sim_t;
+
+int main(int argc, char *argv[]) {
+
+  count_t N = (count_t)1e4;
+
+  D_t D = 2;
+  L_t L = 128;
+  double T = 2.26918531421;
+  double *H_vec = (double *)calloc(MAX_Q, sizeof(double));
+
+  bool silent = false;
+  bool draw = false;
+  unsigned int window_size = 512;
+
+  int opt;
+  q_t H_ind = 0;
+
+  while ((opt = getopt(argc, argv, "N:D:L:T:H:sdw:")) != -1) {
+    switch (opt) {
+    case 'N': // number of steps
+      N = (count_t)atof(optarg);
+      break;
+    case 'D': // dimension
+      D = atoi(optarg);
+      break;
+    case 'L': // linear size
+      L = atoi(optarg);
+      break;
+    case 'T': // temperature 
+      T = atof(optarg);
+      break;
+    case 'H': // external field. nth call couples to state n
+      H_vec[H_ind] = atof(optarg);
+      H_ind++;
+      break;
+    case 's': // don't print anything during simulation. speeds up slightly
+      silent = true;
+      break;
+    case 'd':
+#ifdef HAVE_GLUT
+      draw = true;
+      break;
+#else
+      printf("You didn't compile this with the glut library installed!\n");
+      exit(EXIT_FAILURE);
+#endif
+    case 'w':
+      window_size = atoi(optarg);
+      break;
+    default:
+      exit(EXIT_FAILURE);
+    }
+  }
+
+  // initialize random number generator
+  randutils::auto_seed_128 seeds;
+  std::mt19937 rng{seeds};
+
+  // define spin-spin coupling
+  std::function <double(const potts_t<POTTSQ>&, const potts_t<POTTSQ>&)> Z = [] (const potts_t<POTTSQ>& s1, const potts_t<POTTSQ>& s2) -> double {
+    return cos(2 * M_PI * (double)(s1.x + POTTSQ - s2.x) / (double)POTTSQ);
+  };
+
+  // define spin-field coupling
+  std::function <double(const potts_t<POTTSQ>&)> B = [=] (const potts_t<POTTSQ>& s) -> double {
+    return H_vec[s.x];
+  };
+
+  // initialize state object
+  state_t <dihedral_t<POTTSQ>, potts_t<POTTSQ>> s(D, L, T, Z, B);
+
+  // define function that generates self-inverse rotations
+  std::function <dihedral_t<POTTSQ>(std::mt19937&, potts_t<POTTSQ>)> gen_R = [] (std::mt19937& r, potts_t<POTTSQ> v) -> dihedral_t<POTTSQ> {
+    dihedral_t<POTTSQ> rot;
+    rot.is_reflection = true;
+    std::uniform_int_distribution<q_t> dist(0, POTTSQ - 1);
+    q_t x = dist(r);
+    rot.x = (2 * v.x + x + 1) % POTTSQ;
+
+    return rot;
+  };
+
+  // define function that updates any number of measurements
+  std::function <void(const sim_t&)> measurement;
+
+  double average_M = 0;
+  if (!draw) {
+    // a very simple example: measure the average magnetization
+    measurement = [&] (const sim_t& s) {
+      average_M += (double)s.M[0] / (double)N / (double)s.nv;
+    };
+  } else {
+    // a more complex example: measure the average magnetization, and draw the spin configuration to the screen
+
+#ifdef HAVE_GLUT
+    // initialize glut
+    glutInit(&argc, argv);
+    glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB);
+    glutInitWindowSize(window_size, window_size);
+    glutCreateWindow("wolff");
+    glClearColor(0.0,0.0,0.0,0.0);
+    glMatrixMode(GL_PROJECTION);
+    glLoadIdentity();
+    gluOrtho2D(0.0, L, 0.0, L);
+
+    measurement = [&] (const sim_t& s) {
+      average_M += (double)s.M[0] / (double)N / (double)s.nv;
+      glClear(GL_COLOR_BUFFER_BIT);
+      for (v_t i = 0; i < pow(L, 2); i++) {
+        potts_t<POTTSQ> tmp_s = s.R.act_inverse(s.spins[i]);
+        glColor3f(hue_to_R(tmp_s.x * 2 * M_PI / POTTSQ), hue_to_G(tmp_s.x * 2 * M_PI / POTTSQ), hue_to_B(tmp_s.x * 2 * M_PI / POTTSQ));
+        glRecti(i / L, i % L, (i / L) + 1, (i % L) + 1);
+      }
+      glFlush();
+    };
+#endif
+  }
+
+  // run wolff for N cluster flips
+  wolff(N, s, gen_R, measurement, rng, silent);
+
+  // tell us what we found!
+  printf("%" PRIcount " %d-Potts runs completed. D = %" PRID ", L = %" PRIL ", T = %g, H = %g, <M> = %g\n", N, POTTSQ, D, L, T, H_vec[0], average_M);
+
+  // free the random number generator
+
+  if (draw) {
+  }
+
+  return 0;
+
+}
+
diff --git a/examples/src/models/potts/wolff_potts.cpp b/examples/src/models/potts/wolff_potts.cpp
new file mode 100644
index 0000000..a1e9284
--- /dev/null
+++ b/examples/src/models/potts/wolff_potts.cpp
@@ -0,0 +1,213 @@
+
+#include <getopt.h>
+#include <stdio.h>
+
+#ifdef HAVE_GLUT
+#include <GL/glut.h>
+#endif
+
+// include your group and spin space
+#include "symmetric.hpp"
+#include "potts.hpp"
+
+// hack to speed things up considerably
+#define N_STATES POTTSQ
+#include <wolff/finite_states.hpp>
+
+// include wolff.h
+#include <measure.hpp>
+#include <colors.h>
+#include <randutils/randutils.hpp>
+#include <wolff.hpp>
+
+typedef state_t <symmetric_t<POTTSQ>, potts_t<POTTSQ>> sim_t;
+
+int main(int argc, char *argv[]) {
+
+  count_t N = (count_t)1e4;
+
+  D_t D = 2;
+  L_t L = 128;
+  double T = 2.26918531421;
+  double *H_vec = (double *)calloc(MAX_Q, sizeof(double));
+
+  bool silent = false;
+  bool draw = false;
+  bool N_is_sweeps = false;
+  unsigned int window_size = 512;
+
+  // don't measure anything by default
+  unsigned char measurement_flags = 0;
+
+  int opt;
+  q_t H_ind = 0;
+
+  while ((opt = getopt(argc, argv, "N:D:L:T:H:sdw:M:S")) != -1) {
+    switch (opt) {
+    case 'N': // number of steps
+      N = (count_t)atof(optarg);
+      break;
+    case 'D': // dimension
+      D = atoi(optarg);
+      break;
+    case 'L': // linear size
+      L = atoi(optarg);
+      break;
+    case 'T': // temperature 
+      T = atof(optarg);
+      break;
+    case 'H': // external field. nth call couples to state n
+      H_vec[H_ind] = atof(optarg);
+      H_ind++;
+      break;
+    case 's': // don't print anything during simulation. speeds up slightly
+      silent = true;
+      break;
+    case 'S':
+      N_is_sweeps = true;
+      break;
+    case 'd':
+#ifdef HAVE_GLUT
+      draw = true;
+      break;
+#else
+      printf("You didn't compile this with the glut library installed!\n");
+      exit(EXIT_FAILURE);
+#endif
+    case 'w':
+      window_size = atoi(optarg);
+      break;
+    case 'M':
+      measurement_flags ^= 1 << atoi(optarg);
+      break;
+    default:
+      exit(EXIT_FAILURE);
+    }
+  }
+
+  // get nanosecond timestamp for unique run id
+  unsigned long timestamp;
+
+  {
+    struct timespec spec;
+    clock_gettime(CLOCK_REALTIME, &spec);
+    timestamp = spec.tv_sec*1000000000LL + spec.tv_nsec;
+  }
+
+  // initialize random number generator
+  randutils::auto_seed_128 seeds;
+  std::mt19937 rng{seeds};
+
+  // define spin-spin coupling
+  std::function <double(const potts_t<POTTSQ>&, const potts_t<POTTSQ>&)> Z = [] (const potts_t<POTTSQ>& s1, const potts_t<POTTSQ>& s2) -> double {
+    if (s1.x == s2.x) {
+      return 1.0;
+    } else {
+      return 0.0;
+    }
+  };
+
+  // define spin-field coupling
+  std::function <double(const potts_t<POTTSQ> &)> B = [=] (const potts_t<POTTSQ>& s) -> double {
+    return H_vec[s.x];
+  };
+
+  // initialize state object
+  state_t <symmetric_t<POTTSQ>, potts_t<POTTSQ>> s(D, L, T, Z, B);
+
+  // define function that generates self-inverse rotations
+  std::function <symmetric_t<POTTSQ>(std::mt19937&, potts_t<POTTSQ>)> gen_R = [] (std::mt19937& r, potts_t<POTTSQ> v) -> symmetric_t<POTTSQ> {
+    symmetric_t<POTTSQ> rot;
+
+    std::uniform_int_distribution<q_t> dist(0, POTTSQ - 1);
+    q_t j = dist(r);
+    q_t swap_v;
+    if (j < v.x) {
+      swap_v = j;
+    } else {
+      swap_v = j + 1;
+    }
+
+    rot[v.x] = swap_v;
+    rot[swap_v] = v.x;
+
+    return rot;
+  };
+
+  FILE **outfiles = measure_setup_files(measurement_flags, timestamp);
+
+  std::function <void(const sim_t&)> other_f;
+  uint64_t sum_of_clusterSize = 0;
+
+  if (N_is_sweeps) {
+    other_f = [&] (const sim_t& s) {
+      sum_of_clusterSize += s.last_cluster_size;
+    };
+  } else if (draw) {
+#ifdef HAVE_GLUT
+    // initialize glut
+    glutInit(&argc, argv);
+    glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB);
+    glutInitWindowSize(window_size, window_size);
+    glutCreateWindow("wolff");
+    glClearColor(0.0,0.0,0.0,0.0);
+    glMatrixMode(GL_PROJECTION);
+    glLoadIdentity();
+    gluOrtho2D(0.0, L, 0.0, L);
+
+    other_f = [] (const sim_t& s) {
+      glClear(GL_COLOR_BUFFER_BIT);
+      for (v_t i = 0; i < pow(s.L, 2); i++) {
+        potts_t<POTTSQ> tmp_s = s.R.act_inverse(s.spins[i]);
+        glColor3f(hue_to_R(tmp_s.x * 2 * M_PI / POTTSQ), hue_to_G(tmp_s.x * 2 * M_PI / POTTSQ), hue_to_B(tmp_s.x * 2 * M_PI / POTTSQ));
+        glRecti(i / s.L, i % s.L, (i / s.L) + 1, (i % s.L) + 1);
+      }
+      glFlush();
+    };
+#endif
+  } else {
+    other_f = [] (const sim_t& s) {};
+  }
+
+  std::function <void(const sim_t&)> measurements = measure_function_write_files(measurement_flags, outfiles, other_f);
+
+  // add line to metadata file with run info
+  {
+    FILE *outfile_info = fopen("wolff_metadata.txt", "a");
+
+    fprintf(outfile_info, "<| \"ID\" -> %lu, \"MODEL\" -> \"POTTS\", \"q\" -> %d, \"D\" -> %" PRID ", \"L\" -> %" PRIL ", \"NV\" -> %" PRIv ", \"NE\" -> %" PRIv ", \"T\" -> %.15f, \"H\" -> {", timestamp, POTTSQ, s.D, s.L, s.nv, s.ne, T);
+
+    for (q_t i = 0; i < POTTSQ; i++) {
+      fprintf(outfile_info, "%.15f", H_vec[i]);
+      if (i < POTTSQ - 1) {
+        fprintf(outfile_info, ", ");
+      }
+    }
+
+    fprintf(outfile_info, "} |>\n");
+
+    fclose(outfile_info);
+  }
+
+  // run wolff for N cluster flips
+  if (N_is_sweeps) {
+    count_t N_rounds = 0;
+    printf("\n");
+    while (sum_of_clusterSize < N * s.nv) {
+      printf("\033[F\033[J\033[F\033[JWOLFF: sweep %" PRIu64 " / %" PRIu64 ": E = %.2f, S = %" PRIv "\n", (count_t)((double)sum_of_clusterSize / (double)s.nv), N, s.E, s.last_cluster_size);
+      wolff(N, s, gen_R, measurements, rng, silent);
+      N_rounds++;
+    }
+    printf("\033[F\033[J\033[F\033[JWOLFF: sweep %" PRIu64 " / %" PRIu64 ": E = %.2f, S = %" PRIv "\n\n", (count_t)((double)sum_of_clusterSize / (double)s.nv), N, s.E, s.last_cluster_size);
+  } else {
+    wolff(N, s, gen_R, measurements, rng, silent);
+  }
+
+  // free the random number generator
+  free(H_vec);
+  measure_free_files(measurement_flags, outfiles);
+
+  return 0;
+
+}
+
diff --git a/examples/src/models/roughening/CMakeLists.txt b/examples/src/models/roughening/CMakeLists.txt
new file mode 100644
index 0000000..51a8644
--- /dev/null
+++ b/examples/src/models/roughening/CMakeLists.txt
@@ -0,0 +1,21 @@
+
+add_executable(wolff_dgm             wolff_dgm.cpp)
+add_executable(wolff_cgm             wolff_cgm.cpp)
+
+find_library(GL NAMES GL)
+find_library(GLU NAMES GLU)
+find_library(GLUT NAMES glut)
+
+if (${GLUT} MATCHES "GLUT-NOTFOUND")
+  target_link_libraries(wolff_dgm             wolff wolff_examples)
+  target_link_libraries(wolff_cgm             wolff wolff_examples)
+else()
+  target_compile_definitions(wolff_dgm             PUBLIC HAVE_GLUT)
+  target_compile_definitions(wolff_cgm             PUBLIC HAVE_GLUT)
+
+  target_link_libraries(wolff_dgm             wolff wolff_examples glut GL GLU)
+  target_link_libraries(wolff_cgm             wolff wolff_examples glut GL GLU)
+endif()
+
+install(TARGETS wolff_dgm wolff_cgm DESTINATION ${CMAKE_INSTALL_BINDIR})
+
diff --git a/examples/src/models/roughening/dihedral_inf.hpp b/examples/src/models/roughening/dihedral_inf.hpp
new file mode 100644
index 0000000..19fa195
--- /dev/null
+++ b/examples/src/models/roughening/dihedral_inf.hpp
@@ -0,0 +1,47 @@
+
+#include <wolff/types.h>
+#include <cmath>
+#include "height.hpp"
+
+template <class T>
+class dihedral_inf_t {
+  public:
+  bool is_reflection;
+  T x;
+
+  dihedral_inf_t() : is_reflection(false), x(0) {}
+  dihedral_inf_t(bool x, T y) : is_reflection(x), x(y) {}
+
+  height_t<T> act(const height_t<T>& h) const {
+    if (this->is_reflection) {
+      return height_t(this->x - h.x);
+    } else {
+      return height_t(this->x + h.x);
+    }
+  }
+
+  dihedral_inf_t<T> act(const dihedral_inf_t<T>& r) const {
+    if (this->is_reflection) {
+      return dihedral_inf_t<T>(!r.is_reflection, this->x - r.x);
+    } else {
+      return dihedral_inf_t<T>(r.is_reflection, this->x + r.x);
+    }
+  }
+
+  height_t<T> act_inverse(const height_t<T>& h) const {
+    if (this->is_reflection) {
+      return this->act(h);
+    } else {
+      return height_t(h.x - this->x);
+    }
+  }
+
+  dihedral_inf_t<T> act_inverse(const dihedral_inf_t<T>& r) const {
+    if (this->is_reflection) {
+      return this->act(r);
+    } else {
+      return dihedral_inf_t<T>(r.is_reflection, r.x - this->x);
+    }
+  }
+};
+
diff --git a/examples/src/models/roughening/height.hpp b/examples/src/models/roughening/height.hpp
new file mode 100644
index 0000000..4023063
--- /dev/null
+++ b/examples/src/models/roughening/height.hpp
@@ -0,0 +1,75 @@
+
+#pragma once
+
+#include <cmath>
+#include <stdio.h>
+
+#include <wolff/types.h>
+
+/* The following is the minimum definition of a spin class.
+ *
+ * The class must contain an M_t and an F_t for holding the sum of an
+ * integer number of spins and a double-weighted number of spins,
+ * respectively.
+ *
+ * void init(X_t *p);
+ * void free_spin(X_t p);
+ * void free_spin(M_t p);
+ * void free_spin(F_t p);
+ * X_t copy(X_t x);
+ * void add(M_t *x1, int factor, X_t x2);
+ * void add(F_t *x1, double factor, X_t x2);
+ * M_t scalar_multiple(int factor, X_t x);
+ * F_t scalar_multiple(double factor, X_t x);
+ * double norm_squared(F_t x);
+ * void write_magnetization(M_t M, FILE *outfile);
+ *
+ */
+
+template <class T>
+struct height_t {
+  T x;
+
+  typedef T M_t;
+  typedef double F_t;
+
+  height_t() : x(0) {}
+
+  height_t(T x) : x(x) {}
+
+  inline T operator*(v_t a) const {
+    return x * a;
+  }
+
+  inline double operator*(double a) const {
+    return x * a;
+  }
+
+  inline T operator-(const height_t& h) const {
+    return x - h.x;
+  }
+};
+
+template <class T>
+inline T& operator+=(T& M, const height_t<T> &h) {
+  M += h.x;
+
+  return M;
+}
+
+template <class T>
+inline T& operator-=(T& M, const height_t<T> &h) {
+  M -= h.x;
+
+  return M;
+}
+
+double norm_squared(double h) {
+  return pow(h, 2);
+}
+
+template <class T>
+void write_magnetization(T M, FILE *outfile) {
+  fwrite(&M, sizeof(T), 1, outfile);
+}
+
diff --git a/examples/src/models/roughening/wolff_cgm.cpp b/examples/src/models/roughening/wolff_cgm.cpp
new file mode 100644
index 0000000..65f8d66
--- /dev/null
+++ b/examples/src/models/roughening/wolff_cgm.cpp
@@ -0,0 +1,167 @@
+
+#include <getopt.h>
+
+#ifdef HAVE_GLUT
+#include <GL/glut.h>
+#endif
+
+// include your group and spin space
+#include "dihedral_inf.hpp"
+#include "height.hpp"
+
+#include <randutils/randutils.hpp>
+
+// include wolff.h
+#include <wolff.hpp>
+
+typedef state_t <dihedral_inf_t<double>, height_t<double>> sim_t;
+
+int main(int argc, char *argv[]) {
+
+  count_t N = (count_t)1e4;
+
+  D_t D = 2;
+  L_t L = 128;
+  double T = 2.26918531421;
+  double H = 0;
+
+  bool silent = false;
+  bool draw = false;
+  unsigned int window_size = 512;
+  double epsilon = 1;
+
+  int opt;
+
+  while ((opt = getopt(argc, argv, "N:D:L:T:H:sdw:e:")) != -1) {
+    switch (opt) {
+    case 'N': // number of steps
+      N = (count_t)atof(optarg);
+      break;
+    case 'D': // dimension
+      D = atoi(optarg);
+      break;
+    case 'L': // linear size
+      L = atoi(optarg);
+      break;
+    case 'T': // temperature 
+      T = atof(optarg);
+      break;
+    case 'H': // external field. nth call couples to state n
+      H = atof(optarg);
+      break;
+    case 'e': // external field. nth call couples to state n
+      epsilon = atof(optarg);
+      break;
+    case 's': // don't print anything during simulation. speeds up slightly
+      silent = true;
+      break;
+    case 'd':
+#ifdef HAVE_GLUT
+      draw = true;
+      break;
+#else
+      printf("You didn't compile this with the glut library installed!\n");
+      exit(EXIT_FAILURE);
+#endif
+    case 'w':
+      window_size = atoi(optarg);
+      break;
+    default:
+      exit(EXIT_FAILURE);
+    }
+  }
+
+  // initialize random number generator
+  randutils::auto_seed_128 seeds;
+  std::mt19937 rng{seeds};
+
+  // define spin-spin coupling
+  std::function <double(const height_t<double>&, const height_t<double>&)> Z = [] (const height_t<double>& h1, const height_t<double>& h2) -> double {
+    return -pow(h1.x - h2.x, 2);
+  };
+
+  // define spin-field coupling
+  std::function <double(height_t<double>)> B = [=] (height_t<double> h) -> double {
+    return -H * pow(h.x, 2);;
+  };
+
+  // initialize state object
+  sim_t s(D, L, T, Z, B);
+
+  // define function that generates self-inverse rotations
+  std::function <dihedral_inf_t<double>(std::mt19937&, height_t<double>)> gen_R = [=] (std::mt19937& r, height_t<double> h) -> dihedral_inf_t<double> {
+    dihedral_inf_t<double> rot;
+    rot.is_reflection = true;
+    std::normal_distribution<double> dist(0.0,1.0);
+
+    double amount = epsilon * dist(r);
+
+    rot.x = 2 * h.x + amount;
+
+    return rot;
+  };
+
+  // define function that updates any number of measurements
+  std::function <void(const sim_t&)> measurement;
+
+  double average_M = 0;
+  if (!draw) {
+    // a very simple example: measure the average magnetization
+    measurement = [&] (const sim_t& s) {
+      average_M += (double)s.M / (double)N / (double)s.nv;
+    };
+  } else {
+    // a more complex example: measure the average magnetization, and draw the spin configuration to the screen
+
+#ifdef HAVE_GLUT
+    // initialize glut
+    glutInit(&argc, argv);
+    glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB);
+    glutInitWindowSize(window_size, window_size);
+    glutCreateWindow("wolff");
+    glClearColor(0.0,0.0,0.0,0.0);
+    glMatrixMode(GL_PROJECTION);
+    glLoadIdentity();
+    gluOrtho2D(0.0, L, 0.0, L);
+
+    measurement = [&] (const sim_t& s) {
+      average_M += (double)s.M / (double)N / (double)s.nv;
+      glClear(GL_COLOR_BUFFER_BIT);
+      double max_h = INT64_MIN;
+      double min_h = INT64_MAX;
+      for (v_t i = 0; i < pow(L, 2); i++) {
+        double cur_h = (s.R.act_inverse(s.spins[i])).x;
+        if (cur_h < min_h) {
+          min_h = cur_h;
+        }
+        if (cur_h > max_h) {
+          max_h = cur_h;
+        }
+      }
+
+      for (v_t i = 0; i < pow(L, 2); i++) {
+        double cur_h = (s.R.act_inverse(s.spins[i])).x;
+        double mag = ((double)(cur_h - min_h)) / ((double)(max_h - min_h));
+        glColor3f(mag, mag, mag);
+        glRecti(i / L, i % L, (i / L) + 1, (i % L) + 1);
+      }
+      glFlush();
+    };
+#endif
+  }
+
+  // run wolff for N cluster flips
+  wolff(N, s, gen_R, measurement, rng, silent);
+
+  // tell us what we found!
+  printf("%" PRIcount " DGM runs completed. D = %" PRID ", L = %" PRIL ", T = %g, H = %g, <M> = %g\n", N, D, L, T, H, average_M);
+
+  // free the random number generator
+
+  if (draw) {
+  }
+
+  return 0;
+
+}
+
diff --git a/examples/src/models/roughening/wolff_dgm.cpp b/examples/src/models/roughening/wolff_dgm.cpp
new file mode 100644
index 0000000..8395382
--- /dev/null
+++ b/examples/src/models/roughening/wolff_dgm.cpp
@@ -0,0 +1,164 @@
+
+#include <getopt.h>
+
+#ifdef HAVE_GLUT
+#include <GL/glut.h>
+#endif
+
+// include your group and spin space
+#include "dihedral_inf.hpp"
+#include "height.hpp"
+
+#include <randutils/randutils.hpp>
+
+// include wolff.h
+#include <wolff.hpp>
+
+typedef state_t <dihedral_inf_t<int64_t>, height_t<int64_t>> sim_t;
+
+int main(int argc, char *argv[]) {
+
+  count_t N = (count_t)1e4;
+
+  D_t D = 2;
+  L_t L = 128;
+  double T = 2.26918531421;
+  double H = 0;
+
+  bool silent = false;
+  bool draw = false;
+  unsigned int window_size = 512;
+  uint64_t epsilon = 1;
+
+  int opt;
+
+  while ((opt = getopt(argc, argv, "N:D:L:T:H:sdw:e:")) != -1) {
+    switch (opt) {
+    case 'N': // number of steps
+      N = (count_t)atof(optarg);
+      break;
+    case 'D': // dimension
+      D = atoi(optarg);
+      break;
+    case 'L': // linear size
+      L = atoi(optarg);
+      break;
+    case 'T': // temperature 
+      T = atof(optarg);
+      break;
+    case 'H': // external field. nth call couples to state n
+      H = atof(optarg);
+      break;
+    case 'e': // external field. nth call couples to state n
+      epsilon = atof(optarg);
+      break;
+    case 's': // don't print anything during simulation. speeds up slightly
+      silent = true;
+      break;
+    case 'd':
+#ifdef HAVE_GLUT
+      draw = true;
+      break;
+#else
+      printf("You didn't compile this with the glut library installed!\n");
+      exit(EXIT_FAILURE);
+#endif
+    case 'w':
+      window_size = atoi(optarg);
+      break;
+    default:
+      exit(EXIT_FAILURE);
+    }
+  }
+
+  // initialize random number generator
+  randutils::auto_seed_128 seeds;
+  std::mt19937 rng{seeds};
+
+  // define spin-spin coupling
+  std::function <double(const height_t<int64_t>&, const height_t<int64_t>&)> Z = [] (const height_t<int64_t>& h1, const height_t<int64_t>& h2) -> double {
+    return -pow(h1.x - h2.x, 2);
+  };
+
+  // define spin-field coupling
+  std::function <double(const height_t<int64_t> &)> B = [=] (const height_t<int64_t>& h) -> double {
+    return -H * pow(h.x, 2);;
+  };
+
+  // initialize state object
+  sim_t s(D, L, T, Z, B);
+
+  // define function that generates self-inverse rotations
+  std::function <dihedral_inf_t<int64_t>(std::mt19937&, height_t<int64_t>)> gen_R = [=] (std::mt19937& r, height_t<int64_t> h) -> dihedral_inf_t<int64_t> {
+    dihedral_inf_t<int64_t> rot;
+    rot.is_reflection = true;
+
+    std::uniform_int_distribution<int64_t> dist(-epsilon,epsilon);
+
+    rot.x = 2 * h.x + dist(r);
+
+    return rot;
+  };
+
+  // define function that updates any number of measurements
+  std::function <void(const sim_t&)> measurement;
+
+  double average_M = 0;
+  if (!draw) {
+    // a very simple example: measure the average magnetization
+    measurement = [&] (const sim_t& s) {
+      average_M += (double)s.M / (double)N / (double)s.nv;
+    };
+  } else {
+    // a more complex example: measure the average magnetization, and draw the spin configuration to the screen
+
+#ifdef HAVE_GLUT
+    // initialize glut
+    glutInit(&argc, argv);
+    glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB);
+    glutInitWindowSize(window_size, window_size);
+    glutCreateWindow("wolff");
+    glClearColor(0.0,0.0,0.0,0.0);
+    glMatrixMode(GL_PROJECTION);
+    glLoadIdentity();
+    gluOrtho2D(0.0, L, 0.0, L);
+
+    measurement = [&] (const sim_t& s) {
+      average_M += (double)s.M / (double)N / (double)s.nv;
+      glClear(GL_COLOR_BUFFER_BIT);
+      int64_t max_h = INT64_MIN;
+      int64_t min_h = INT64_MAX;
+      for (v_t i = 0; i < pow(L, 2); i++) {
+        int64_t cur_h = (s.R.act_inverse(s.spins[i])).x;
+        if (cur_h < min_h) {
+          min_h = cur_h;
+        }
+        if (cur_h > max_h) {
+          max_h = cur_h;
+        }
+      }
+
+      for (v_t i = 0; i < pow(L, 2); i++) {
+        int64_t cur_h = (s.R.act_inverse(s.spins[i])).x;
+        double mag = ((double)(cur_h - min_h)) / ((double)(max_h - min_h));
+        glColor3f(mag, mag, mag);
+        glRecti(i / L, i % L, (i / L) + 1, (i % L) + 1);
+      }
+      glFlush();
+    };
+#endif
+  }
+
+  // run wolff for N cluster flips
+  wolff(N, s, gen_R, measurement, rng, silent);
+
+  // tell us what we found!
+  printf("%" PRIcount " DGM runs completed. D = %" PRID ", L = %" PRIL ", T = %g, H = %g, <M> = %g\n", N, D, L, T, H, average_M);
+
+  if (draw) {
+  }
+
+  return 0;
+
+}
+
diff --git a/examples/src/tools/CMakeLists.txt b/examples/src/tools/CMakeLists.txt
new file mode 100644
index 0000000..1c73c2d
--- /dev/null
+++ b/examples/src/tools/CMakeLists.txt
@@ -0,0 +1,7 @@
+
+find_library(fftw REQUIRED NAMES fftw3)
+
+add_executable(analyze_correlations analyze_correlations.cpp)
+
+target_link_libraries(analyze_correlations fftw3 wolff)
+
diff --git a/examples/src/tools/analyze_correlations.cpp b/examples/src/tools/analyze_correlations.cpp
new file mode 100644
index 0000000..abeaff3
--- /dev/null
+++ b/examples/src/tools/analyze_correlations.cpp
@@ -0,0 +1,486 @@
+
+#include <wolff/types.h>
+#include <cmath>
+#include <cstring>
+#include <stdio.h>
+#include <stdlib.h>
+#include <getopt.h>
+#include <fftw3.h>
+
+template <class T>
+double mean(int N, T *data) {
+  double total = 0;
+  for (int i = 0; i < N; i++) {
+    total += (double)data[i];
+  }
+
+  return total / N;
+}
+
+double squared_mean(int N, double *data) {
+  double total = 0;
+  for (int i = 0; i < N; i++) {
+    total += pow(data[i], 2);
+  }
+
+  return total / N;
+}
+
+double central_moment(int N, double *data, double mean, int m) {
+  double total = 0;
+  for (int i = 0; i < N; i++) {
+    total += pow(data[i] - mean, m);
+  }
+
+  return total / N;
+}
+
+void compute_OO(int N, fftw_plan forward_plan, double *forward_data, fftw_plan reverse_plan, double *reverse_data) {
+
+  fftw_execute(forward_plan);
+
+  reverse_data[0] = forward_data[0] * forward_data[0];
+  reverse_data[N / 2] = forward_data[N/2] * forward_data[N/2];
+
+  for (count_t i = 1; i < N / 2; i++) {
+    reverse_data[i] = pow(forward_data[i], 2) + pow(forward_data[N - i], 2);
+    reverse_data[N - i] = 0;
+  }
+
+  fftw_execute(reverse_plan);
+
+}
+
+double finite_energy(q_t nb, double *J, q_t q, double *H, v_t nv, v_t ne, uint32_t *bo, uint32_t *so) {
+  double energy = 0;
+
+  v_t tot = 0;
+  for (q_t i = 0; i < nb - 1; i++) {
+    energy -= J[i] * bo[i];
+    tot += bo[i];
+  }
+
+  energy -= J[nb - 1] * (ne - tot);
+
+  tot = 0;
+  for (q_t i = 0; i < q - 1; i++) {
+    energy -= H[i] * so[i];
+    tot += so[i];
+  }
+
+  energy -= H[q - 1] * (nv - tot);
+
+  return energy;
+}
+
+int main (int argc, char *argv[]) {
+  count_t drop = (count_t)1e4;
+  count_t length = (count_t)1e4;
+  bool speedy_drop = false;
+  bool from_stdin = false;
+  bool oldstyle = false;
+
+  int opt;
+
+  while ((opt = getopt(argc, argv, "d:l:spo")) != -1) {
+    switch (opt) {
+      case 'd':
+        drop = (count_t)atof(optarg);
+        break;
+      case 'l':
+        length = (count_t)atof(optarg);
+        break;
+      case 's':
+        speedy_drop = true;
+        break;
+      case 'p':
+        from_stdin = true;
+        break;
+      case 'o':
+        oldstyle = true;
+        break;
+      default:
+        exit(EXIT_FAILURE);
+    }
+  }
+  FILE *metadata;
+
+  fftw_set_timelimit(1);
+
+  if (from_stdin) {
+    metadata = stdin;
+  } else {
+    metadata = fopen("wolff_metadata.txt", "r");
+  }
+
+  if (metadata == NULL) {
+    printf("Metadata file not found. Make sure you are in the correct directory!\n");
+    exit(EXIT_FAILURE);
+  }
+
+  unsigned long id;
+  char *model = (char *)malloc(32 * sizeof(char));
+
+  if (model == NULL) {
+    printf("Malloc failed.\n");
+    exit(EXIT_FAILURE);
+  }
+
+  q_t q;
+  D_t D;
+  L_t L;
+  v_t nv, ne;
+
+ while (EOF != fscanf(metadata, "<| \"ID\" -> %lu, \"MODEL\" -> \"%[^\"]\", \"q\" -> %" SCNq ", \"D\" -> %" SCND ", \"L\" -> %" SCNL ", \"NV\" -> %" SCNv ", \"NE\" -> %" SCNv ", ", &id, model, &q, &D, &L, &nv, &ne)) {
+
+   printf("%lu: Processing...\n", id);
+
+//   bool is_finite = 0 == strcmp(model, "ISING") || 0 == strcmp(model, "POTTS") || 0 == strcmp(model, "CLOCK");
+
+    if (oldstyle) {
+      q_t nb;
+      double T;
+      fscanf(metadata, "\"NB\" -> %" SCNq ", \"T\" -> %lf, \"J\" -> {", &nb, &T);
+      double *J = (double *)malloc(nb * sizeof(double));
+      double *H = (double *)malloc(q * sizeof(double));
+
+      if (J == NULL || H == NULL) {
+        printf("%lu: Malloc failed.\n", id);
+        break;
+      }
+
+      for (q_t i = 0; i < nb - 1; i++) {
+        fscanf(metadata, "%lf, ", &(J[i]));
+      }
+      fscanf(metadata, "%lf}, \"H\" -> {", &(J[nb - 1]));
+      for (q_t i = 0; i < q - 1; i++) {
+        fscanf(metadata, "%lf, ", &(H[i]));
+      }
+      fscanf(metadata, "%lf} |>\n", &(H[q - 1]));
+
+      char *filename_M = (char *)malloc(128 * sizeof(char));
+      char *filename_B = (char *)malloc(128 * sizeof(char));
+      char *filename_S = (char *)malloc(128 * sizeof(char));
+
+      if (filename_M == NULL || filename_B == NULL || filename_S == NULL) {
+        printf("%lu: Malloc failed.\n", id);
+        break;
+      }
+
+      sprintf(filename_M, "wolff_%lu_M.dat", id);
+      sprintf(filename_B, "wolff_%lu_B.dat", id);
+      sprintf(filename_S, "wolff_%lu_S.dat", id);
+
+      FILE *file_M = fopen(filename_M, "rb");
+      FILE *file_B = fopen(filename_B, "rb");
+      FILE *file_S = fopen(filename_S, "rb");
+
+      if (file_M == NULL || file_B == NULL || file_S == NULL) {
+        printf("%lu: Opening data file failed.\n", id);
+        break;
+      }
+
+      fseek(file_S, 0, SEEK_END);
+      unsigned long N = ftell(file_S) / sizeof(uint32_t);
+      fseek(file_S, 0, SEEK_SET);
+
+      if (speedy_drop) {
+        drop = N - pow(2, floor(log(N) / log(2)));
+      } else {
+        if (N % 2 == 1 && drop % 2 == 0) {
+          drop++; // make sure M is even
+        }
+      }
+
+      if (N <= drop) {
+        printf("\033[F%lu: Number of steps %lu is less than %" PRIcount ", nothing done.\n", id, N, drop);
+      } else {
+        int M = N - drop;
+
+        double M_f = (double)M;
+
+        if (length > M) {
+          length = M;
+        }
+
+        double *forward_data = (double *)fftw_malloc(M * sizeof(double));
+        fftw_plan forward_plan = fftw_plan_r2r_1d(M, forward_data, forward_data, FFTW_R2HC, 0);
+        double *reverse_data = (double *)fftw_malloc(M * sizeof(double));
+        fftw_plan reverse_plan = fftw_plan_r2r_1d(M, reverse_data, reverse_data, FFTW_HC2R, 0);
+
+
+        uint32_t *data_S = (uint32_t *)malloc(N * sizeof(uint32_t));
+        fread(data_S, N, sizeof(uint32_t), file_S);
+        for (count_t i = 0; i < M; i++) {
+          forward_data[i] = (double)data_S[drop + i];
+        }
+        free(data_S);
+        double mean_S = mean(M, forward_data);
+        double squaredMean_S = squared_mean(M, forward_data);
+        double moment2_S = central_moment(M, forward_data, mean_S, 2);
+        double moment4_S = central_moment(M, forward_data, mean_S, 4);
+
+        compute_OO(M, forward_plan, forward_data, reverse_plan, reverse_data);
+
+        sprintf(filename_S, "wolff_%lu_S_OO.dat", id);
+
+        FILE *file_S = fopen(filename_S, "wb");
+        fwrite(&M_f, sizeof(double), 1, file_S);
+        fwrite(&mean_S, sizeof(double), 1, file_S);
+        fwrite(&squaredMean_S, sizeof(double), 1, file_S);
+        fwrite(&moment2_S, sizeof(double), 1, file_S);
+        fwrite(&moment4_S, sizeof(double), 1, file_S);
+        fwrite(reverse_data, sizeof(double), length, file_S);
+        fclose(file_S);
+
+        uint32_t *data_B = (uint32_t *)malloc((nb - 1) * N * sizeof(uint32_t));
+        uint32_t *data_M = (uint32_t *)malloc((q - 1) * N * sizeof(uint32_t));
+        fread(data_B, N * (nb - 1), sizeof(uint32_t), file_B);
+        fread(data_M, N * (q - 1), sizeof(uint32_t), file_M);
+
+        for (count_t i = 0; i < M; i++) {
+          forward_data[i] = finite_energy(nb, J, q, H, nv, ne, data_B + (nb - 1) * (drop + i), data_M + (q - 1) * (drop + i));
+        }
+
+        double mean_E = mean(M, forward_data);
+        double squaredMean_E = squared_mean(M, forward_data);
+        double moment2_E = central_moment(M, forward_data, mean_E, 2);
+        double moment4_E = central_moment(M, forward_data, mean_E, 4);
+
+        free(data_B);
+        free(data_M);
+
+        compute_OO(M, forward_plan, forward_data, reverse_plan, reverse_data);
+
+        sprintf(filename_B, "wolff_%lu_E_OO.dat", id);
+
+        FILE *file_E = fopen(filename_B, "wb");
+        fwrite(&M_f, sizeof(double), 1, file_E);
+        fwrite(&mean_E, sizeof(double), 1, file_E);
+        fwrite(&squaredMean_E, sizeof(double), 1, file_E);
+        fwrite(&moment2_E, sizeof(double), 1, file_E);
+        fwrite(&moment4_E, sizeof(double), 1, file_E);
+        fwrite(reverse_data, sizeof(double), length, file_E);
+        fclose(file_E);
+
+        printf("\033[F%lu: Correlation functions for %d steps written.\n", id, M);
+
+        fftw_destroy_plan(forward_plan);
+        fftw_destroy_plan(reverse_plan);
+        fftw_free(forward_data);
+        fftw_free(reverse_data);
+
+      }
+
+      fclose(file_M);
+      fclose(file_B);
+      fclose(file_S);
+
+      free(J);
+      free(H);
+
+      free(filename_S);
+      free(filename_B);
+      free(filename_M);
+
+    } else {
+      char *junk = (char *)malloc(1024 * sizeof(char));
+      fscanf(metadata, "%[^\n]\n", junk); // throw away the rest of the line, we don't need it
+      free(junk);
+
+      char *filename_E = (char *)malloc(128 * sizeof(char));
+      char *filename_F = (char *)malloc(128 * sizeof(char));
+      char *filename_M = (char *)malloc(128 * sizeof(char));
+      char *filename_S = (char *)malloc(128 * sizeof(char));
+
+      sprintf(filename_E, "wolff_%lu_E.dat", id);
+      sprintf(filename_F, "wolff_%lu_F.dat", id);
+      sprintf(filename_M, "wolff_%lu_M.dat", id);
+      sprintf(filename_S, "wolff_%lu_S.dat", id);
+
+      FILE *file_E = fopen(filename_E, "rb");
+      FILE *file_F = fopen(filename_F, "rb");
+      FILE *file_M = fopen(filename_M, "rb");
+      FILE *file_S = fopen(filename_S, "rb");
+
+      fseek(file_S, 0, SEEK_END);
+      unsigned long N = ftell(file_S) / sizeof(uint32_t);
+      fseek(file_S, 0, SEEK_SET);
+
+      if (speedy_drop) {
+        drop = N - pow(2, floor(log(N) / log(2)));
+      } else {
+        if (N % 2 == 1 && drop % 2 == 0) {
+          drop++; // make sure M is even
+        }
+      }
+
+      if (N <= drop) {
+        printf("\033[F%lu: Number of steps %lu is less than %" PRIcount ", nothing done.\n", id, N, drop);
+      } else {
+        int M = N - drop;
+        double M_f = (double)M;
+
+        if (length > M) {
+          length = M;
+        }
+
+        double *forward_data = (double *)fftw_malloc(M * sizeof(double));
+        fftw_plan forward_plan = fftw_plan_r2r_1d(M, forward_data, forward_data, FFTW_R2HC, 0);
+
+        double *reverse_data = (double *)fftw_malloc(M * sizeof(double));
+        fftw_plan reverse_plan = fftw_plan_r2r_1d(M, reverse_data, reverse_data, FFTW_HC2R, 0);
+
+        if (file_S != NULL) {
+          uint32_t *data_S = (uint32_t *)malloc(N * sizeof(uint32_t));
+
+          fread(data_S, sizeof(uint32_t), N, file_S);
+          fclose(file_S);
+
+          for (int i = 0; i < M; i++) {
+            forward_data[i] = (double)data_S[drop + i];
+          }
+          free(data_S);
+
+          double mean_S = mean(M, forward_data);
+          double squaredMean_S = squared_mean(M, forward_data);
+          double moment2_S = central_moment(M, forward_data, mean_S, 2);
+          double moment4_S = central_moment(M, forward_data, mean_S, 4);
+
+          compute_OO(M, forward_plan, forward_data, reverse_plan, reverse_data);
+
+          sprintf(filename_S, "wolff_%lu_S_OO.dat", id);
+          FILE *file_S_new = fopen(filename_S, "wb");
+          fwrite(&M_f, sizeof(double), 1, file_S_new);
+          fwrite(&mean_S, sizeof(double), 1, file_S_new);
+          fwrite(&squaredMean_S, sizeof(double), 1, file_S_new);
+          fwrite(&moment2_S, sizeof(double), 1, file_S_new);
+          fwrite(&moment4_S, sizeof(double), 1, file_S_new);
+          fwrite(reverse_data, sizeof(double), length, file_S_new);
+          fclose(file_S_new);
+        }
+        if (file_F != NULL) {
+          float *data_F = (float *)malloc(N * sizeof(float));
+
+          fread(data_F, sizeof(float), N, file_F);
+          fclose(file_F);
+
+          for (int i = 0; i < M; i++) {
+            forward_data[i] = (double)data_F[drop + i];
+          }
+          free(data_F);
+
+          double mean_F = mean(M, forward_data);
+          double squaredMean_F = squared_mean(M, forward_data);
+          double moment2_F = central_moment(M, forward_data, mean_F, 2);
+          double moment4_F = central_moment(M, forward_data, mean_F, 4);
+
+          compute_OO(M, forward_plan, forward_data, reverse_plan, reverse_data);
+
+          sprintf(filename_F, "wolff_%lu_F_OO.dat", id);
+          FILE *file_F_new = fopen(filename_F, "wb");
+          fwrite(&M_f, sizeof(double), 1, file_F_new);
+          fwrite(&mean_F, sizeof(double), 1, file_F_new);
+          fwrite(&squaredMean_F, sizeof(double), 1, file_F_new);
+          fwrite(&moment2_F, sizeof(double), 1, file_F_new);
+          fwrite(&moment4_F, sizeof(double), 1, file_F_new);
+          fwrite(reverse_data, sizeof(double), length, file_F_new);
+          fclose(file_F_new);
+        }
+        if (file_E != NULL) {
+          float *data_E = (float *)malloc(N * sizeof(float));
+
+          fread(data_E, sizeof(float), N, file_E);
+          fclose(file_E);
+
+          for (int i = 0; i < M; i++) {
+            forward_data[i] = (double)data_E[drop + i];
+          }
+          free(data_E);
+
+          double mean_E = mean(M, forward_data);
+          double squaredMean_E = squared_mean(M, forward_data);
+          double moment2_E = central_moment(M, forward_data, mean_E, 2);
+          double moment4_E = central_moment(M, forward_data, mean_E, 4);
+
+          compute_OO(M, forward_plan, forward_data, reverse_plan, reverse_data);
+
+          sprintf(filename_E, "wolff_%lu_E_OO.dat", id);
+          FILE *file_E_new = fopen(filename_E, "wb");
+          fwrite(&M_f, sizeof(double), 1, file_E_new);
+          fwrite(&mean_E, sizeof(double), 1, file_E_new);
+          fwrite(&squaredMean_E, sizeof(double), 1, file_E_new);
+          fwrite(&moment2_E, sizeof(double), 1, file_E_new);
+          fwrite(&moment4_E, sizeof(double), 1, file_E_new);
+          fwrite(reverse_data, sizeof(double), length, file_E_new);
+          fclose(file_E_new);
+        }
+        if (file_M != NULL) {
+          if (0 == strcmp(model, "PLANAR")) {
+            float *data_M = (float *)malloc(2 * N * sizeof(float));
+            fread(data_M, sizeof(float), 2 * N, file_M);
+            fclose(file_M);
+            for (int i = 0; i < M; i++) {
+              forward_data[i] = (double)sqrt(pow(data_M[2 * drop + 2 * i], 2) + pow(data_M[2 * drop + 2 * i + 1], 2));
+            }
+            free(data_M);
+          } else if (0 == strcmp(model, "HEISENBERG")) {
+            float *data_M = (float *)malloc(3 * N * sizeof(float));
+            fread(data_M, sizeof(float), 3 * N, file_M);
+            fclose(file_M);
+            for (int i = 0; i < M; i++) {
+              forward_data[i] = sqrt(pow(data_M[3 * drop + 3 * i], 2) + pow(data_M[3 * drop + 3 * i + 1], 2) + pow(data_M[3 * drop + 3 * i + 2], 2));
+            }
+            free(data_M);
+          } else if (0 == strcmp(model, "ISING")) {
+            int *data_M = (int *)malloc(N * sizeof(float));
+            fread(data_M, sizeof(int), N, file_M);
+            fclose(file_M);
+            for (int i = 0; i < M; i++) {
+              forward_data[i] = (double)data_M[i];
+            }
+            free(data_M);
+          } else {
+            printf("UNKNOWN MODEL\n");
+            exit(EXIT_FAILURE);
+          }
+
+          double mean_M = mean(M, forward_data);
+          double squaredMean_M = squared_mean(M, forward_data);
+          double moment2_M = central_moment(M, forward_data, mean_M, 2);
+          double moment4_M = central_moment(M, forward_data, mean_M, 4);
+
+          compute_OO(M, forward_plan, forward_data, reverse_plan, reverse_data);
+
+          sprintf(filename_M, "wolff_%lu_M_OO.dat", id);
+          FILE *file_M_new = fopen(filename_M, "wb");
+          fwrite(&M_f, sizeof(double), 1, file_M_new);
+          fwrite(&mean_M, sizeof(double), 1, file_M_new);
+          fwrite(&squaredMean_M, sizeof(double), 1, file_M_new);
+          fwrite(&moment2_M, sizeof(double), 1, file_M_new);
+          fwrite(&moment4_M, sizeof(double), 1, file_M_new);
+          fwrite(reverse_data, sizeof(double), length, file_M_new);
+          fclose(file_M_new);
+        }
+
+        printf("\033[F%lu: Correlation functions for %d steps written.\n", id, M);
+        fftw_destroy_plan(forward_plan);
+        fftw_destroy_plan(reverse_plan);
+        fftw_free(forward_data);
+        fftw_free(reverse_data);
+
+      }
+      free(filename_E);
+      free(filename_S);
+      free(filename_F);
+      free(filename_M);
+    }
+  }
+
+  free(model);
+  fclose(metadata);
+  fftw_cleanup();
+
+  return 0;
+}
+