many changes, including new spin spaces and groups and cleaning up core library code

15 files changed, 464 insertions, 23 deletions

diff --git a/CMakeLists.txt b/CMakeLists.txt
index fe564f7..12fe087 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -22,6 +22,7 @@ add_executable(wolff_4potts src/wolff_potts.cpp ${CPPSOURCES} ${CSOURCES})
 add_executable(wolff_7potts src/wolff_potts.cpp ${CPPSOURCES} ${CSOURCES})
 add_executable(wolff_3clock src/wolff_clock.cpp ${CPPSOURCES} ${CSOURCES})
 add_executable(wolff_5clock src/wolff_clock.cpp ${CPPSOURCES} ${CSOURCES})
+add_executable(wolff_planar2 src/wolff_O2.cpp ${CPPSOURCES} ${CSOURCES})
 add_executable(wolff_planar src/wolff_On.cpp ${CPPSOURCES} ${CSOURCES})
 add_executable(wolff_heisenberg src/wolff_On.cpp ${CPPSOURCES} ${CSOURCES})
 add_executable(analyze_correlations src/analyze_correlations.cpp ${CPPSOURCES} ${CSOURCES})
@@ -54,6 +55,7 @@ if (${GLUT} MATCHES "GLUT-NOTFOUND")
   target_link_libraries(wolff_5clock cblas gsl m)
   target_link_libraries(wolff_heisenberg cblas gsl m)
   target_link_libraries(wolff_planar cblas gsl m)
+  target_link_libraries(wolff_planar2 cblas gsl m)
 else()
   target_link_libraries(wolff_ising cblas gsl m glut GL GLU)
   target_link_libraries(wolff_dgm cblas gsl m glut GL GLU)
@@ -65,6 +67,7 @@ else()
   target_link_libraries(wolff_5clock cblas gsl m glut GL GLU)
   target_link_libraries(wolff_heisenberg cblas gsl m glut GL GLU)
   target_link_libraries(wolff_planar cblas gsl m glut GL GLU)
+  target_link_libraries(wolff_planar2 cblas gsl m glut GL GLU)
   target_compile_definitions(wolff_ising PUBLIC HAVE_GLUT)
   target_compile_definitions(wolff_dgm PUBLIC HAVE_GLUT)
   target_compile_definitions(wolff_cgm PUBLIC HAVE_GLUT)
@@ -74,6 +77,7 @@ else()
   target_compile_definitions(wolff_3clock PUBLIC HAVE_GLUT)
   target_compile_definitions(wolff_5clock PUBLIC HAVE_GLUT)
   target_compile_definitions(wolff_planar PUBLIC HAVE_GLUT)
+  target_compile_definitions(wolff_planar2 PUBLIC HAVE_GLUT)
   target_compile_definitions(wolff_heisenberg PUBLIC HAVE_GLUT)
 endif()
 
diff --git a/lib/angle.h b/lib/angle.h
new file mode 100644
index 0000000..c3f128e
--- /dev/null
+++ b/lib/angle.h
@@ -0,0 +1,48 @@
+#pragma once
+
+#include "types.h"
+
+#include <cmath>
+#include "vector.h"
+
+class angle_t {
+  public:
+    double x;
+
+    typedef vector_t<2, double> M_t;
+    typedef vector_t<2, double> F_t;
+
+    angle_t() : x(0) {}
+    angle_t(double x) : x(x) {}
+
+    inline vector_t<2, double> operator*(v_t a) const {
+      vector_t<2, double>M;
+      M[0] = a * cos(x);
+      M[1] = a * sin(x);
+
+      return M;
+    }
+
+    inline vector_t<2, double> operator*(double a) const {
+      vector_t<2, double>M;
+      M[0] = a * cos(x);
+      M[1] = a * sin(x);
+
+      return M;
+    }
+};
+
+inline vector_t<2,double>& operator+=(vector_t<2,double>& M, const angle_t& theta) {
+  M[0] += cos(theta.x);
+  M[1] += sin(theta.x);
+
+  return M;
+}
+
+inline vector_t<2,double>& operator-=(vector_t<2,double>& M, const angle_t& theta) {
+  M[0] -= cos(theta.x);
+  M[1] -= sin(theta.x);
+
+  return M;
+}
+
diff --git a/lib/circle_group.h b/lib/circle_group.h
new file mode 100644
index 0000000..cb7cadd
--- /dev/null
+++ b/lib/circle_group.h
@@ -0,0 +1,46 @@
+#pragma once
+
+#include "angle.h"
+
+class circle_group_t {
+  public:
+    bool is_reflection;
+    double x;
+
+    circle_group_t() : is_reflection(false), x(0) {}
+    circle_group_t(bool x, double y) : is_reflection(x), x(y) {}
+
+    angle_t act(const angle_t& theta) const {
+      if (is_reflection) {
+        return angle_t(fmod(2 * M_PI + x - theta.x, 2 * M_PI));
+      } else {
+        return angle_t(fmod(x + theta.x, 2 * M_PI));
+      }
+    }
+
+    circle_group_t act(const circle_group_t& r) const {
+      if (is_reflection) {
+        return circle_group_t(!r.is_reflection, fmod(2 * M_PI + x - r.x, 2 * M_PI));
+      } else {
+        return circle_group_t(r.is_reflection, fmod(x + r.x, 2 * M_PI));
+      }
+    }
+
+    angle_t act_inverse(const angle_t& theta) const {
+      if (is_reflection) {
+        return act(theta);
+      } else {
+        return angle_t(fmod(2 * M_PI + theta.x - x, 2 * M_PI));
+      }
+    }
+
+    circle_group_t act_inverse(const circle_group_t& r) const {
+      if (is_reflection) {
+        return act(r);
+      } else {
+        return circle_group_t(r.is_reflection, fmod(2 * M_PI + r.x - x, 2 * M_PI));
+      }
+    }
+};
+
+
diff --git a/lib/cluster.h b/lib/cluster.h
index c5f2be7..f948586 100644
--- a/lib/cluster.h
+++ b/lib/cluster.h
@@ -31,7 +31,9 @@ void flip_cluster(state_t <R_t, X_t> *state, v_t v0, R_t r, gsl_rng *rand) {
       R_old = state->R;
       marks[v] = true;
 
-      if (v == state->nv) {
+      bool v_is_ghost = (v == state->nv);
+
+      if (v_is_ghost) {
         R_new = r.act(R_old);
       } else {
         si_old = state->spins[v];
@@ -40,19 +42,18 @@ void flip_cluster(state_t <R_t, X_t> *state, v_t v0, R_t r, gsl_rng *rand) {
 
       for (const v_t &vn : state->g.v_adj[v]) {
         X_t sj;
+        bool vn_is_ghost = (vn == state->nv);
 
-        if (vn != state->nv) {
+        if (!vn_is_ghost) {
           sj = state->spins[vn];
         }
 
         double prob;
 
-        bool is_ext = (v == state->nv || vn == state->nv);
-
-        if (is_ext) {
+        if (v_is_ghost || vn_is_ghost) {
           X_t rs_old, rs_new;
           v_t non_ghost;
-          if (vn == state->nv) {
+          if (vn_is_ghost) {
             rs_old = R_old.act_inverse(si_old);
             rs_new = R_old.act_inverse(si_new);
             non_ghost = v;
@@ -61,6 +62,7 @@ void flip_cluster(state_t <R_t, X_t> *state, v_t v0, R_t r, gsl_rng *rand) {
             rs_new = R_new.act_inverse(sj);
             non_ghost = vn;
           }
+
           double dE = state->H(rs_old) - state->H(rs_new);
 #ifdef FINITE_STATES
           prob = H_probs[state_to_ind(rs_old)][state_to_ind(rs_new)];
@@ -97,7 +99,7 @@ void flip_cluster(state_t <R_t, X_t> *state, v_t v0, R_t r, gsl_rng *rand) {
         }
       }
 
-      if (v == state->nv) {
+      if (v_is_ghost) {
         state->R = R_new;
       } else {
         state->spins[v] = si_new;
diff --git a/lib/dihedral.h b/lib/dihedral.h
index 5588afa..8d0472b 100644
--- a/lib/dihedral.h
+++ b/lib/dihedral.h
@@ -21,7 +21,6 @@ class dihedral_t {
       }
     }
 
-
     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); 
diff --git a/lib/state.h b/lib/state.h
index eefa0cb..5abf65b 100644
--- a/lib/state.h
+++ b/lib/state.h
@@ -27,10 +27,10 @@ class state_t {
     std::vector<double> precomputed_cos;
     std::vector<double> precomputed_sin;
 
-    std::function <double(X_t, X_t)> J;
-    std::function <double(X_t)> H;
+    std::function <double(const X_t&, const X_t&)> J;
+    std::function <double(const X_t&)> H;
 
-    state_t(D_t D, L_t L, double T, std::function <double(X_t, X_t)> J, std::function <double(X_t)> H) : D(D), L(L), g(D, L), T(T), R(), J(J), H(H) {
+    state_t(D_t D, L_t L, double T, std::function <double(const X_t&, const X_t&)> J, std::function <double(const X_t&)> H) : D(D), L(L), g(D, L), T(T), R(), J(J), H(H) {
       nv = g.nv;
       ne = g.ne;
       g.add_ext();
diff --git a/lib/torus.h b/lib/torus.h
new file mode 100644
index 0000000..2aead52
--- /dev/null
+++ b/lib/torus.h
@@ -0,0 +1,64 @@
+
+#pragma once
+
+#include <cmath>
+#include <array>
+#include "types.h"
+
+template <q_t n>
+class torus_t : public std::array<double, n> {
+  public:
+    typedef std::array<double, n> M_t;
+    typedef std::array<double, n> F_t;
+
+    torus_t() {
+      this->fill(0);
+    }
+
+    inline torus_t<n> operator*(v_t a) const {
+      torus_t<n> x;
+      for (q_t i = 0; i < n; i++) {
+        x[i] = a * (*this)[i];
+      }
+
+      return x;
+    }
+
+    inline torus_t<n> operator*(double a) const {
+      torus_t<n> x;
+      for (q_t i = 0; i < n; i++) {
+        x[i] = a * (*this)[i];
+      }
+
+      return x;
+    }
+
+    inline torus_t<n>& operator+=(const torus_t<n>& x) {
+      for (q_t i = 0; i < n; i++) {
+        (*this)[i] += x[i];
+      }
+    }
+
+    inline torus_t<n>& operator-=(const torus_t<n>& x) {
+      for (q_t i = 0; i < n; i++) {
+        (*this)[i] -= x[i];
+      }
+    }
+};
+
+template <q_t n>
+double norm_squared(const torus_t<n>& x) {
+  double tmp = 0;
+  for (const double& xi : x) {
+    tmp += pow(xi, 2);
+  }
+  return tmp;
+}
+
+void write_magnetization(const torus_t<n>& x, FILE *outfile) {
+  for (const double& xi : x) {
+    float tmp_xi = (float)xi;
+    fwrite(&tmp_xi, sizeof(float), 1, outfile);
+  }
+}
+
diff --git a/lib/vector.h b/lib/vector.h
index beee1a7..2f4077a 100644
--- a/lib/vector.h
+++ b/lib/vector.h
@@ -109,7 +109,7 @@ void write_magnetization(vector_t <q, double> M, FILE *outfile) {
 }
 
 template <q_t q, class T>
-T dot(vector_t <q, T> v1, vector_t <q, T> v2) {
+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++) {
@@ -120,7 +120,7 @@ T dot(vector_t <q, T> v1, vector_t <q, T> v2) {
 }
 
 template <q_t q, class T>
-double H_vector(vector_t <q, T> v1, T *H) {
+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));
 }
diff --git a/src/wolff_O2.cpp b/src/wolff_O2.cpp
new file mode 100644
index 0000000..63ca0a7
--- /dev/null
+++ b/src/wolff_O2.cpp
@@ -0,0 +1,278 @@
+
+#include <getopt.h>
+#include <stdio.h>
+
+#ifdef HAVE_GLUT
+#include <GL/glut.h>
+#endif
+
+#include <circle_group.h>
+#include <angle.h>
+
+#include <wolff.h>
+#include <measure.h>
+#include <colors.h>
+#include <rand.h>
+
+typedef circle_group_t orthogonal_R_t;
+typedef angle_t vector_R_t;
+typedef state_t <orthogonal_R_t, vector_R_t> On_t;
+
+double H_modulated(vector_R_t v, int order, double mag) {
+  return mag * cos(order * v.x);
+}
+
+double theta(double *v) {
+  double x = v[0];
+  double y = v[1];
+
+  if (x == 0) { 
+    if (y >= 0) {
+      return M_PI / 2;
+    } else {
+      return - M_PI / 2;
+    }
+  } else {
+    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;
+    }
+  }
+}
+
+int main(int argc, char *argv[]) {
+
+  count_t N = (count_t)1e7;
+
+  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 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;
+    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 '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(gsl_rng *, vector_R_t)> gen_R;
+
+  if (use_pert) {
+    gen_R = [=] (gsl_rng *r, const angle_t& t) -> circle_group_t {
+      circle_group_t rot;
+      rot.is_reflection = true;
+
+      unsigned int x = gsl_rng_uniform_int(r, order);
+      double amount = epsilon * gsl_ran_ugaussian(r);
+
+      rot.x = fmod(2 * M_PI * (1.0 + (double)x / (double)order + amount), 2 * M_PI);
+
+      return rot;
+    };
+    pert_type = "PERTURB";
+  } else {
+    gen_R = [=] (gsl_rng *r, const angle_t& t) -> circle_group_t {
+      circle_group_t rot;
+      rot.is_reflection = true;
+      rot.x = 2 * M_PI * gsl_rng_uniform(r);
+
+      return rot;
+    };
+    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[2], 2, 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 < 2; i++) {
+      fprintf(outfile_info, "%.15f", H_vec[i]);
+      if (i < 2 - 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 saturation = 0.7;
+        double value = 0.9;
+        double chroma = saturation * value;
+        glColor3f(chroma * hue_to_R(v_tmp.x) + (value - chroma), chroma * hue_to_G(v_tmp.x) + (value - chroma), chroma * hue_to_B(v_tmp.x) + (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 angle_t&, const angle_t&)> J = [] (const angle_t& t1, const angle_t& t2) -> double {
+    return cos(t1.x - t2.x);
+  };
+
+  std::function <double(const angle_t &)> H;
+
+  if (modulated_field) {
+    H = [=] (const angle_t& t) -> double {
+      return H_vec[0] * cos(order * t.x);
+    };
+  } else {
+    double mag = 0;
+    for (q_t i = 0; i < 2; i++) {
+      mag += pow(H_vec[i], 2);
+    }
+    mag = sqrt(mag);
+    double t0 = theta(H_vec);
+    H = [=] (const angle_t& t) -> double {
+      return mag * cos(t0 + t.x);
+    };
+  }
+
+  // initialize random number generator
+  gsl_rng *r = gsl_rng_alloc(gsl_rng_taus2);
+  gsl_rng_set(r, rand_seed());
+
+  state_t <orthogonal_R_t, vector_R_t> s(D, L, T, J, H);
+
+  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, r, 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, r, silent);
+  }
+
+  measure_free_files(measurement_flags, outfiles);
+  free(H_vec);
+  gsl_rng_free(r);
+
+  return 0;
+}
+
diff --git a/src/wolff_On.cpp b/src/wolff_On.cpp
index 5458860..cbde498 100644
--- a/src/wolff_On.cpp
+++ b/src/wolff_On.cpp
@@ -206,7 +206,7 @@ int main(int argc, char *argv[]) {
 
   std::function <void(const On_t *)> measurements = measure_function_write_files(measurement_flags, outfiles, other_f);
 
-  std::function <double(vector_R_t)> H;
+  std::function <double(const vector_R_t&)> H;
 
   if (modulated_field) {
     H = std::bind(H_modulated, std::placeholders::_1, order, H_vec[0]);
diff --git a/src/wolff_cgm.cpp b/src/wolff_cgm.cpp
index 7613691..ec3ae36 100644
--- a/src/wolff_cgm.cpp
+++ b/src/wolff_cgm.cpp
@@ -75,7 +75,7 @@ int main(int argc, char *argv[]) {
   gsl_rng_set(r, rand_seed());
 
   // define spin-spin coupling
-  std::function <double(height_t<double>, height_t<double>)> Z = [] (height_t<double> h1, height_t<double> h2) -> double {
+  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);
   };
 
diff --git a/src/wolff_clock.cpp b/src/wolff_clock.cpp
index bc2c5d1..376eaec 100644
--- a/src/wolff_clock.cpp
+++ b/src/wolff_clock.cpp
@@ -78,12 +78,12 @@ int main(int argc, char *argv[]) {
   gsl_rng_set(r, rand_seed());
 
   // define spin-spin coupling
-  std::function <double(potts_t<POTTSQ>, potts_t<POTTSQ>)> Z = [] (potts_t<POTTSQ> s1, potts_t<POTTSQ> s2) -> double {
+  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(potts_t<POTTSQ>)> B = [=] (potts_t<POTTSQ> s) -> double {
+  std::function <double(const potts_t<POTTSQ>&)> B = [=] (const potts_t<POTTSQ>& s) -> double {
     return H_vec[s.x];
   };
 
diff --git a/src/wolff_dgm.cpp b/src/wolff_dgm.cpp
index 2583704..d00cae5 100644
--- a/src/wolff_dgm.cpp
+++ b/src/wolff_dgm.cpp
@@ -75,12 +75,12 @@ int main(int argc, char *argv[]) {
   gsl_rng_set(r, rand_seed());
 
   // define spin-spin coupling
-  std::function <double(height_t<int64_t>, height_t<int64_t>)> Z = [] (height_t<int64_t> h1, height_t<int64_t> h2) -> double {
+  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(height_t<int64_t>)> B = [=] (height_t<int64_t> h) -> double {
+  std::function <double(const height_t<int64_t> &)> B = [=] (const height_t<int64_t>& h) -> double {
     return -H * pow(h.x, 2);;
   };
 
diff --git a/src/wolff_ising.cpp b/src/wolff_ising.cpp
index 410e046..0c9485d 100644
--- a/src/wolff_ising.cpp
+++ b/src/wolff_ising.cpp
@@ -99,7 +99,7 @@ int main(int argc, char *argv[]) {
   gsl_rng_set(r, rand_seed());
 
   // define spin-spin coupling
-  std::function <double(ising_t, ising_t)> Z = [] (ising_t s1, ising_t s2) -> double {
+  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 {
@@ -108,7 +108,7 @@ int main(int argc, char *argv[]) {
   };
 
   // define spin-field coupling
-  std::function <double(ising_t)> B = [=] (ising_t s) -> double {
+  std::function <double(const ising_t&)> B = [=] (const ising_t& s) -> double {
     if (s.x) {
       return -H;
     } else {
diff --git a/src/wolff_potts.cpp b/src/wolff_potts.cpp
index 07663d5..2bc306b 100644
--- a/src/wolff_potts.cpp
+++ b/src/wolff_potts.cpp
@@ -99,7 +99,7 @@ int main(int argc, char *argv[]) {
   gsl_rng_set(r, rand_seed());
 
   // define spin-spin coupling
-  std::function <double(potts_t<POTTSQ>, potts_t<POTTSQ>)> Z = [] (potts_t<POTTSQ> s1, potts_t<POTTSQ> s2) -> double {
+  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 {
@@ -108,7 +108,7 @@ int main(int argc, char *argv[]) {
   };
 
   // define spin-field coupling
-  std::function <double(potts_t<POTTSQ>)> B = [=] (potts_t<POTTSQ> s) -> double {
+  std::function <double(const potts_t<POTTSQ> &)> B = [=] (const potts_t<POTTSQ>& s) -> double {
     return H_vec[s.x];
   };