Initial commit.

1 files changed, 341 insertions, 0 deletions

diff --git a/glass.cpp b/glass.cpp
new file mode 100644
index 0000000..e0c5e25
--- /dev/null
+++ b/glass.cpp
@@ -0,0 +1,341 @@
+#include <iostream>
+#include <vector>
+#include <list>
+#include <set>
+#include <eigen3/Eigen/Dense>
+
+#include "pcg-cpp/include/pcg_random.hpp"
+#include "randutils/randutils.hpp"
+
+using Rng = randutils::random_generator<pcg32>;
+
+template<int D> using Vector = Eigen::Matrix<int, D, 1>;
+template<int D> using Matrix = Eigen::Matrix<int, D, D>;
+
+int iPow(int x, unsigned p) {
+  if (p == 0) return 1;
+  if (p == 1) return x;
+
+  int tmp = iPow(x, p / 2);
+  if (p % 2 == 0) return tmp * tmp;
+  else return x * tmp * tmp;
+}
+
+unsigned mod(signed a, unsigned b) {
+  return ((a %= b) < 0) ? a + b : a;
+}
+
+template<unsigned D> class State {
+  public:
+    Vector<D> σ;
+
+    State(unsigned a, signed b) : σ(Vector<D>::Zero()) {
+      σ[a] = b;
+    }
+
+    State<D> apply(const Matrix<D>& m) const {
+      return {m * σ};
+    }
+};
+
+template <unsigned D> class Vertex;
+
+template<unsigned D> class Particle {
+  public:
+    Vertex<D>& position;
+    State<D> state;
+    bool marked;
+
+    Particle(Vertex<D>& p, const State<D>& s) : position(p), state(s) {}
+};
+
+template<unsigned D> State<D> randomState(Rng& r) {
+  return State<D>(r.uniform((unsigned)0, D - 1), r.pick({-1, 1}));
+}
+
+template<unsigned D> class HalfEdge {
+  public:
+    Vertex<D>& neighbor;
+    Vector<D> Δx;
+
+    HalfEdge(Vertex<D>& n, const Vector<D>& d) : neighbor(n), Δx(d) {}
+};
+
+template<unsigned D> class Vertex {
+  public:
+    Vector<D> position;
+    std::vector<HalfEdge<D>> adjacentEdges;
+    Particle<D>* occupant;
+
+    bool empty() const {
+      return occupant == NULL;
+    }
+};
+
+template<unsigned D> class System {
+  public:
+    const unsigned L;
+    std::vector<Vertex<D>> vertices;
+    std::set<Particle<D>*> particles;
+
+    unsigned vectorToIndex(const Vector<D>& x) const {
+      unsigned i = 0;
+      for (unsigned d = 0; d < D; d++) {
+        i += x[d] * iPow(L, d);
+      }
+      return i;
+    }
+
+    Vector<D> indexToVector(unsigned i) const {
+      Vector<D> x;
+      for (unsigned d = 0; d < D; d++) {
+        x[d] = (i / iPow(L, d)) % L;
+      }
+      return x;
+    }
+
+    unsigned N() const {
+      return particles.size();
+    }
+
+    System(unsigned L) : L(L), vertices(iPow(L, D)) {
+      for (unsigned i = 0; i < iPow(L, D); i++) {
+        vertices[i].position = indexToVector(i);
+        vertices[i].adjacentEdges.reserve(2 * D);
+        vertices[i].occupant = NULL;
+      }
+
+      for (unsigned d = 0; d < D; d++) {
+        Vector<D> Δx = Vector<D>::Zero();
+        Δx[d] = 1;
+        for (signed i = 0; i < iPow(L, D); i++) {
+          unsigned j = iPow(L, d + 1) * (i / iPow(L, d + 1)) + mod(i + iPow(L, d), pow(L, d + 1));
+          vertices[i].adjacentEdges.push_back(HalfEdge<D>(vertices[j], Δx));
+          vertices[j].adjacentEdges.push_back(HalfEdge<D>(vertices[i], -Δx));
+        }
+      }
+    }
+
+    std::list<Particle<D>*> overlaps(const Particle<D>& p, bool excludeSelf = false) const {
+      std::list<Particle<D>*> o;
+
+      if (!p.position.empty() && !excludeSelf) {
+        o.push_back(p.position.occupant);
+      }
+
+      for (const HalfEdge<D>& e : p.position.adjacentEdges) {
+        if (!e.neighbor.empty()) {
+          if (p.state.σ.dot(e.Δx) == 1 || e.neighbor.occupant->state.σ.dot(e.Δx) == -1) {
+            o.push_back(e.neighbor.occupant);
+          } 
+        }
+      }
+
+      return o;
+    }
+
+    bool insert(const Particle<D>& p) {
+      if (overlaps(p).empty()) {
+        Particle<D>* pN = new Particle<D>(p);
+        particles.insert(pN);
+        p.position.occupant = pN;
+        return true;
+      } else {
+        return false;
+      }
+    }
+
+    void remove(Particle<D>* p) {
+      p->position.occupant = NULL;
+      particles.erase(p);
+      delete p;
+    }
+
+    /*
+    bool randomMove(Rng& r) {
+      Particle<D>& p = *(r.pick(particles));
+      Particle<D> pN = p;
+
+      if (0.2 < r.uniform(0.0, 1.0)) {
+        pN.position = r.pick(p.position.adjacentEdges).neighbor;
+      }
+      pN.state = randomState<D>(r);
+
+      if (overlaps(pN, true).empty()) {
+        remove(&p);
+        insert(pN);
+        return true;
+      } else {
+        return false;
+      }
+    }
+    */
+
+    bool swap(Particle<D>& p1, Particle<D>& p2) {
+      std::swap(p1.state, p2.state);
+      if (overlaps(p1, true).empty() && overlaps(p2, true).empty()) {
+        return true;
+      } else {
+        std::swap(p1.state, p2.state);
+        return false;
+      }
+    }
+
+    bool randomSwap(Rng& r) {
+      return swap(*r.pick(particles), *r.pick(particles));
+    }
+
+    void setGroundState() {
+      for (Particle<D>* p : particles) {
+        remove(p);
+      }
+
+      for (Vertex<D>& v : vertices) {
+        unsigned a = 0;
+        for (unsigned d = 0; d < D; d++) {
+          a += (d + 1) * v.position(d);
+        }
+        a %= 2 * D + 1;
+
+        if (a > 0) {
+          if (a <= D) {
+            State<D> s(a - 1, -1);
+            insert(Particle<D>(v, s));
+          } else if (D < a) {
+            State<D> s(2 * D - a, 1);
+            insert(Particle<D>(v, s));
+          }
+        }
+      }
+    }
+
+    bool compatible() {
+      for (Particle<D>* p : particles) {
+        if (!overlaps(*p, true).empty()) {
+          return false;
+        }
+      }
+
+      return true;
+    }
+
+    double density() const {
+      return N() / pow(L, D);
+    }
+
+    unsigned maxOccupation() const {
+//      return (2 * D * iPow(L, D)) / (2 * D + 1);
+      return iPow(L, D);
+    }
+
+    void sweepGrandCanonical(double z, Rng& r) {
+      for (unsigned i = 0; i < iPow(L, D); i++) {
+        if (0.5 < r.uniform(0.0, 1.0)) {
+          double pIns = maxOccupation() * z / (N() + 1);
+
+          if (pIns > r.uniform(0.0, 1.0)) {
+            while (true) {
+              Vertex<D>& v = r.pick(vertices);
+              if (v.empty()) {
+                insert(Particle<D>(v, randomState<D>(r)));
+                break;
+              }
+            }
+          }
+        } else {
+
+          double pDel = N() / (z * maxOccupation());
+
+          if (pDel > r.uniform(0.0, 1.0)) {
+            remove(r.pick(particles));
+          }
+        }
+
+//        randomMove(r);
+        randomSwap(r);
+      }
+    }
+
+    void sweepLocal(double z, Rng& r) {
+      for (unsigned i = 0; i < iPow(L, D); i++) {
+//        randomMove(r);
+      }
+    }
+
+    void sweepSwap(double z, Rng& r) {
+      for (unsigned i = 0; i < iPow(L, D); i++) {
+        randomSwap(r);
+      }
+    }
+
+    void flipCluster(const Matrix<D>& R, Vertex<D>& v0, Rng& r, bool dry = false) {
+      std::list<std::reference_wrapper<Vertex<D>>> q = {v0};
+
+      while (!q.empty()) {
+        Vertex<D>& v = q.front();
+        q.pop_front();
+
+        Vector<D> xNew = R * v.position;
+        State<D> sNew = v.state.apply(R);
+
+        for (Vertex<D>& vn : overlaps(vertices[vectorToIndex(xNew)], sNew)) {
+          if (!vn.marked) {
+            vn.marked = true;
+            q.push_back(vn);
+          }
+        }
+      }
+    }
+};
+
+template<unsigned D> Vector<D> randomVector(unsigned L, Rng& r) {
+  Vector<D> x;
+  for (unsigned i = 0; i < D; i++) {
+    x[i] = r.uniform((unsigned)0, L - 1);
+  }
+  return x;
+}
+
+int main() {
+  const unsigned D = 3;
+  unsigned L = 28;
+  unsigned Nmin = 2e2;
+  unsigned Nmax = 2e5;
+  double Tmin = 0.04;
+  double Tmax = 0.2;
+  double δT = 0.02;
+
+  System<D> s(L);
+
+  Rng r;
+
+  for (unsigned N = Nmin; N <= Nmax; N *= 10) {
+    s.setGroundState();
+    if (!s.compatible()) {
+      return 1;
+    }
+    for (double T = Tmin; T < Tmax; T *= 1 + δT) {
+      double z = exp(1 / T);
+
+      for (unsigned n = 0; n < N; n++) {
+        s.sweepGrandCanonical(z, r);
+      }
+
+      std::cout << L << " " << T << " " << N << " " << δT << " " << 1 / s.density() << std::endl;
+    }
+
+    for (double T = Tmax; T > Tmin; T /= 1 + δT) {
+      double z = exp(1 / T);
+
+      for (unsigned n = 0; n < N; n++) {
+        s.sweepGrandCanonical(z, r);
+      }
+
+      std::cout << L << " " << T << " " << N << " " << δT << " " << 1 / s.density() << std::endl;
+    }
+  }
+
+  return 0;
+}
+
+