Started implementing dimers on a torus

3 files changed, 158 insertions, 107 deletions

diff --git a/dimers_torus.cpp b/dimers_torus.cpp
new file mode 100644
index 0000000..f304564
--- /dev/null
+++ b/dimers_torus.cpp
@@ -0,0 +1,137 @@
+
+#include <chrono>
+#include <fstream>
+#include <iostream>
+
+#include "animation.hpp"
+#include "space_wolff.hpp"
+#include "spheres.hpp"
+#include "torus_symmetries.hpp"
+
+const unsigned D = 2;
+typedef Model<double, D, TorusGroup<double, D>, Dimer<double, 2>> model;
+
+Gen<double, D, TorusGroup<double, D>, Dimer<double, D>> eGen(double L) {
+  std::vector<Vector<double, 2>> torusVectors = torus_vecs<double, 2>(L);
+  std::vector<Matrix<double, 2>> torusMatrices = torus_mats<double, 2>();
+  return [L, torusVectors,
+          torusMatrices](Model<double, D, TorusGroup<double, D>, Dimer<double, D>>& M,
+                         Rng& r) -> Transformation<double, D, TorusGroup<double, D>, Dimer<double, D>>* {
+    Matrix<double, 2> m;
+    Vector<double, 2> t;
+
+    m = r.pick(torusMatrices);
+    t(0) = r.uniform<double>(0, L);
+    t(1) = r.uniform<double>(0, L);
+    t = t - m * t;
+
+    TorusGroup<double, 2> g = TorusGroup<double, 2>({(double)L, t, m});
+
+    Spin<double, 2, Dimer<double, 2>>* ss = r.pick(M.s);
+
+    return new SpinFlip<double, 2, TorusGroup<double, 2>, Dimer<double, 2>>(M, g, ss);
+  };
+}
+
+int main(int argc, char* argv[]) {
+  const unsigned D = 2;
+
+  double L = 32;
+  unsigned N = 1000;
+  double T = 2.0 / log(1.0 + sqrt(2.0));
+  double H = 1.0;
+  unsigned n = 25;
+  unsigned wait = 1000;
+
+  double k = 1e2;
+  double a = 0.1;
+
+  int opt;
+
+  while ((opt = getopt(argc, argv, "n:N:L:T:H:a:k:w:")) != -1) {
+    switch (opt) {
+    case 'n':
+      n = (unsigned)atof(optarg);
+      break;
+    case 'N':
+      N = (unsigned)atof(optarg);
+      break;
+    case 'L':
+      L = atof(optarg);
+      break;
+    case 'T':
+      T = atof(optarg);
+      break;
+    case 'H':
+      H = atof(optarg);
+      break;
+    case 'a':
+      a = atof(optarg);
+      break;
+    case 'k':
+      k = atof(optarg);
+      break;
+    case 'w':
+      wait = atoi(optarg);
+      break;
+    default:
+      exit(1);
+    }
+  }
+
+  auto zSingle = zSpheresTorus<D>(L, a, k);
+
+  std::function<double(const Spin<double, D, Dimer<double, D>>&,
+                       const Spin<double, D, Dimer<double, D>>&)>
+      Z = [L, zSingle, a, k](const Spin<double, D, Dimer<double, D>>& s1,
+                          const Spin<double, D, Dimer<double, D>>& s2) -> double {
+    Spin<double, D, Radius> s11 = {.x = s1.x + s1.s.relativePosition, .s = s1.s.radius};
+    Spin<double, D, Radius> s12 = {.x = s1.x - s1.s.relativePosition, .s = s1.s.radius};
+    Spin<double, D, Radius> s21 = {.x = s2.x + s2.s.relativePosition, .s = s2.s.radius};
+    Spin<double, D, Radius> s22 = {.x = s2.x - s2.s.relativePosition, .s = s2.s.radius};
+
+    return zSingle(s11, s21) + zSingle(s12, s21) + zSingle(s11, s22) + zSingle(s12, s22);
+  };
+
+  std::function<double(Spin<double, D, Dimer<double, D>>)> B = [L, H](Spin<double, D, Dimer<double, D>> s) -> double {
+    return H * s.x(1);
+  };
+
+  auto g1 = eGen(L);
+
+  auto tag = std::chrono::high_resolution_clock::now();
+
+  Animation<double, D, TorusGroup<double, D>, Dimer<double, D>> A(L, 750, argc, argv, wait, true);
+  model sphere(L, Z, B);
+
+  Rng rng;
+
+  sphere.s.resize(n);
+
+  unsigned nx = floor(sqrt(n));
+  for (unsigned i = 0; i < sphere.s.size(); i++) {
+    Spin<double, 2, Dimer<double, D>>* ss = new Spin<double, 2, Dimer<double, D>>();
+    ss->x = {(i / nx) * L / nx - L / 2, (i % nx) * L / nx - L / 2};
+    ss->s = Dimer<double, D>{.relativePosition = {0.2, 0}, .radius = 0.25};
+    sphere.s[i] = ss;
+    sphere.dict.insert(ss);
+  }
+
+  sphere.wolff(T, {g1}, A, N);
+
+  /*
+  std::ofstream snapfile;
+  snapfile.open("sphere_snap.dat");
+
+  for (Spin<double, D, double>* s : sphere.s) {
+    Spin<double, D, double> rs = sphere.s0.inverse().act(*s);
+    snapfile << rs.s << " " << rs.x.transpose() << "\n";
+    delete s;
+  }
+
+  snapfile.close();
+  */
+
+  return 0;
+}
+
diff --git a/spheres.cpp b/spheres.cpp
index 4235d66..0067cc8 100644
--- a/spheres.cpp
+++ b/spheres.cpp
@@ -5,116 +5,11 @@
 
 #include "space_wolff.hpp"
 #include "torus_symmetries.hpp"
+#include "animation.hpp"
 
 const unsigned D = 2;
 typedef Model<double, D, TorusGroup<double, D>, double> model;
 
-class animation : public measurement<double, 2, TorusGroup<double, D>, double> {
-private:
-  uint64_t t1;
-  uint64_t t2;
-  unsigned n;
-  unsigned tmp;
-  unsigned wait;
-  double L;
-  TorusGroup<double, D> s0_tmp;
-  std::ofstream& file;
-
-public:
-  animation(double L, unsigned w, int argc, char* argv[], unsigned wait, std::ofstream& file) : s0_tmp(0), wait(wait), L(50 * L), file(file) {
-    t1 = 0;
-    t2 = 0;
-    n = 0;
-
-    glutInit(&argc, argv);
-    glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB);
-    glutInitWindowSize(w, w);
-    glutCreateWindow("wolffWindow");
-    glClearColor(0.0, 0.0, 0.0, 0.0);
-    glMatrixMode(GL_PROJECTION);
-    glLoadIdentity();
-    gluOrtho2D(-1, L+1, -1, L+1);
-  }
-
-  void pre_cluster(const model& m, unsigned, const Transformation<double, D, TorusGroup<double, D>, double>* t) override {
-    s0_tmp = m.s0.inverse();
-    tmp = 0;
-    glClearColor(1.0f, 1.0f, 1.0f, 1.0f);
-    glClear(GL_COLOR_BUFFER_BIT);
-    glColor3d(1.0, 0.0, 0.0);
-    glBegin(GL_LINES);
-      Vector<double, 2> r = t->r.t / 2;
-      double θ = atan2(r(1), r(0));
-      Vector<double, 2> v1 = s0_tmp.act({r(0) + L * sin(θ), r(1) - L * cos(θ)});
-      Vector<double, 2> v2 = s0_tmp.act({r(0) - L * sin(θ), r(1) + L * cos(θ)});
-      glVertex2d(v1(0), v1(1));
-      glVertex2d(v2(0), v2(1));
-      if (n > wait)
-        file << v1.transpose() << " " << v2.transpose() << std::endl;
-    glEnd();
-    for (const Spin<double, 2, double>* s : m.s) {
-      glBegin(GL_POLYGON);
-      unsigned n_points = 50;
-      glColor3f(0.0f, 0.0f, 0.0f);
-      if (n > wait)
-        file << s << " " << s->s << " " << s0_tmp.act(*s).x.transpose() << " ";
-      for (unsigned i = 0; i < n_points; i++) {
-        glVertex2d(s0_tmp.act(*s).x(0) + s->s * cos(2 * i * M_PI / n_points),
-                   s0_tmp.act(*s).x(1) + s->s * sin(2 * i * M_PI / n_points));
-      }
-      glEnd();
-    }
-    if (n > wait)
-      file << std::endl;
-    glLineWidth(3);
-    glFlush();
-  }
-
-  void plain_site_transformed(const model& m, const Transformation<double, D, TorusGroup<double, D>, double>& t) override {
-    if (n > wait) {
-      if (t.current().size() > 1) {
-        glColor3f(0.0f, 0.0f, 1.0f);
-      } else {
-        glColor3f(0.0f, 1.0f, 0.0f);
-      }
-      for (const Spin<double, 2, double>* s : t.current()) {
-        if (s != NULL) {
-          file << s << " " << s0_tmp.act(t.r.act(*s)).x.transpose() << " ";
-          glBegin(GL_POLYGON);
-          unsigned n_points = 50;
-          for (unsigned i = 0; i < n_points; i++) {
-            glVertex2d(s0_tmp.act(*s).x(0) + s->s * cos(2 * i * M_PI / n_points),
-                       s0_tmp.act(*s).x(1) + s->s * sin(2 * i * M_PI / n_points));
-          }
-          glEnd();
-        } else {
-          file << s << " " << s0_tmp.act({0, 0}).transpose() << " ";
-        }
-      }
-    }
-    tmp++;
-  }
-
-  void post_cluster(const model& m) override {
-    t1 += tmp;
-    t2 += tmp * tmp;
-    if (n > wait) {
-      file << std::endl;
-      glFlush();
-      sleep(2);
-    }
-    n++;
-  }
-
-  void clear() {
-    t1 = 0;
-    t2 = 0;
-    n = 0;
-  }
-
-  double var() { return (t2 - t1 * t1 / (double)n) / (double)n; }
-};
-
 Gen<double, D, TorusGroup<double, D>, double> eGen(double L) {
   std::vector<Vector<double, 2>> torusVectors = torus_vecs<double, 2>(L);
   std::vector<Matrix<double, 2>> torusMatrices = torus_mats<double, 2>();
@@ -196,7 +91,7 @@ int main(int argc, char* argv[]) {
 
   auto g = eGen(L);
   std::ofstream ofile("test.dat");
-  animation A(L, 750, argc, argv, 1000, ofile);
+  Animation<double, D, TorusGroup<double, D>, Radius> A(L, 750, argc, argv, 1000, true);
   model sphere(L, Z, B);
 
   randutils::mt19937_rng rng;
diff --git a/spheres.hpp b/spheres.hpp
index 040313c..3dc4a5e 100644
--- a/spheres.hpp
+++ b/spheres.hpp
@@ -20,6 +20,25 @@ zSpheres(double a, double k) {
   };
 }
 
+template <int D>
+std::function<double(const Spin<double, D, Radius>&, const Spin<double, D, Radius>&)>
+zSpheresTorus(double L, double a, double k) {
+      return [L, a, k](const Spin<double, D, double>& s1, const Spin<double, D, double>& s2) -> double {
+    Vector<double, D> d = diff(L, s1.x, s2.x);
+
+    double σ = s1.s + s2.s;
+    double δ = σ - sqrt(d.transpose() * d);
+
+    if (δ > -a * σ) {
+      return 0.5 * k * (2 * pow(a * σ, 2) - pow(δ, 2));
+    } else if (δ > -2 * a * σ) {
+      return 0.5 * k * pow(δ + 2 * a * σ, 2);
+    } else {
+      return 0;
+    }
+  };
+}
+
 template <int D, class S> std::function<double(Spin<double, D, S>)> bCenter(double H) {
   return [H](Spin<double, D, S> s) -> double { return H * s.x.norm(); };
 }