1
2
3
4
5
6
7
8
9
10
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
|
#include <GL/glut.h>
#include <fstream>
#include <iostream>
#include "space_wolff.hpp"
#include "torus_symmetries.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;
public:
animation(double L, unsigned w, int argc, char* argv[]) {
t1 = 0;
t2 = 0;
n = 0;
glutInit(&argc, argv);
glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB);
glutInitWindowSize(w, w);
glutCreateWindow("wolff");
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&, unsigned, const TorusGroup<double, D>&) override { tmp = 0; }
void plain_site_transformed(const model&, const Spin<double, D, double>*,
const Spin<double, D, double>&) override {
tmp++;
}
void post_cluster(const model& m) override {
glClearColor(1.0f, 1.0f, 1.0f, 1.0f);
glClear(GL_COLOR_BUFFER_BIT);
for (const Spin<double, 2, double>& s : m.s) {
glBegin(GL_POLYGON);
unsigned n_points = 50;
glColor3f(0.0f, 0.0f, 0.0f);
for (unsigned i = 0; i < n_points; i++) {
glVertex2d(m.s0.inverse().act(s).x(0) + s.s * cos(2 * i * M_PI / n_points),
m.s0.inverse().act(s).x(1) + s.s * sin(2 * i * M_PI / n_points));
}
glEnd();
}
glFlush();
t1 += tmp;
t2 += tmp * tmp;
n++;
}
void clear() {
t1 = 0;
t2 = 0;
n = 0;
}
double var() { return (t2 - t1 * t1 / (double)n) / (double)n; }
};
std::function<TorusGroup<double, D>(const model&, randutils::mt19937_rng&)>
eGen(const std::vector<Matrix<double, 2>>& mats, const std::vector<Vector<double, 2>>& vecs,
double ε, double L) {
return
[&mats, &vecs, L, ε](const model& M, randutils::mt19937_rng& rng) -> TorusGroup<double, 2> {
Vector<double, D> t;
Matrix<double, D> m;
unsigned flip = rng.uniform((unsigned)0, (unsigned)(mats.size() + vecs.size() - 1));
if (flip < mats.size()) {
unsigned f_ind = rng.uniform((unsigned)0, (unsigned)M.s.size());
t = M.s[f_ind].x;
for (unsigned j = 0; j < D; j++) {
t(j) = fmod(10 * L + t(j) + rng.variate<double, std::normal_distribution>(0.0, ε), L);
}
m = mats[flip];
} else {
for (unsigned j = 0; j < D; j++) {
for (unsigned k = 0; k < D; k++) {
if (j == k) {
m(j, k) = 1;
} else {
m(j, k) = 0;
}
}
}
t = vecs[flip - mats.size()];
}
TorusGroup<double, D> g(M.L, t, m);
return g;
};
}
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;
int opt;
while ((opt = getopt(argc, argv, "n:N:L:T:H:")) != -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;
default:
exit(1);
}
}
double k = 1e2;
double a = 0.05;
std::function<double(const Spin<double, D, double>&, const Spin<double, D, double>&)> Z =
[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;
}
};
std::function<double(Spin<double, D, double>)> B = [L, H](Spin<double, D, double> s) -> double {
return H * s.x(1);
};
std::vector<Matrix<double, D>> mats = torus_mats<double, D>();
std::vector<Vector<double, D>> vecs = torus_vecs<double, D>(L);
auto g = eGen(mats, vecs, L, L);
animation A(L, 750, argc, argv);
model sphere(L, Z, B);
randutils::mt19937_rng rng;
sphere.s.reserve(n);
unsigned nx = floor(sqrt(n));
for (unsigned i = 0; i < n; i++) {
Vector<double, D> pos = {(i / nx) * L / nx, (i % nx) * L / nx};
sphere.s.push_back({pos, 0.5});
sphere.dict.insert(&sphere.s.back());
}
sphere.wolff(T, g, A, N);
std::ofstream outfile;
outfile.open("test.dat");
for (signed i = -10; i <= 10; i++) {
A.clear();
double ε = pow(2, -4 + i / 2.0);
auto gn = eGen(mats, vecs, ε, L);
sphere.wolff(T, gn, A, N);
outfile << ε << " " << A.var() / sphere.s.size() << std::endl;
std::cout << ε << " " << A.var() / sphere.s.size() << std::endl;
}
outfile.close();
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.x.transpose() << "\n";
}
snapfile.close();
return 0;
}
|
