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
|
#include "space_wolff.hpp"
template <int D>
std::function<double(const Spin<double, D, Radius>&, const Spin<double, D, Radius>&)>
zSpheres(double a, double k) {
return [a, k](const Spin<double, D, Radius>& s1, const Spin<double, D, Radius>& s2) -> double {
Vector<double, D> d = 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(); };
}
template <int D> Euclidean<double, D> flipAround(double θ, Vector<double, D>& t₀) {
Matrix<double, D> m;
m(0, 0) = -cos(2 * θ);
m(1, 1) = cos(2 * θ);
m(0, 1) = -2 * cos(θ) * sin(θ);
m(1, 0) = -2 * cos(θ) * sin(θ);
return Euclidean<double, D>(t₀ - m * t₀, m);
}
template <int D, class S> Gen<double, D, Euclidean<double, D>, S> nudgeGen(double ε) {
return [ε](Model<double, D, Euclidean<double, D>, S>& M,
Rng& rng) -> Transformation<double, D, Euclidean<double, D>, S>* {
double θ = rng.uniform((double)0.0, 2 * M_PI);
Spin<double, D, S>* s = rng.pick(M.s);
Vector<double, D> t = s->x;
for (unsigned j = 0; j < D; j++) {
t(j) += rng.variate<double, std::normal_distribution>(0.0, ε);
}
return new SpinFlip<double, D, Euclidean<double, D>, S>(M, flipAround(θ, t), s);
};
}
template <int D, class S> Gen<double, D, Euclidean<double, D>, S> swapGen(double ε) {
return [ε](Model<double, D, Euclidean<double, D>, S>& M,
Rng& rng) -> Transformation<double, D, Euclidean<double, D>, S>* {
Spin<double, D, S>* s1 = rng.pick(M.s);
Spin<double, D, S>* s2 = rng.pick(M.s);
while (s1 == s2) {
s2 = rng.pick(M.s);
}
Vector<double, D> t1 = s1->x;
Vector<double, D> t2 = s2->x;
Vector<double, D> t12 = t1 - t2;
Vector<double, D> t = (t1 + t2) / 2;
double θ =
atan2(t12(1), t12(0)) + rng.variate<double, std::normal_distribution>(0.0, ε) / t12.norm();
return new PairFlip<double, D, Euclidean<double, D>, S>(M, flipAround(θ, t), s1, s2);
};
}
template <int D, class S> Gen<double, D, Euclidean<double, D>, S> accrossGen(double ε) {
return [ε](Model<double, D, Euclidean<double, D>, S>& M,
Rng& rng) -> Transformation<double, D, Euclidean<double, D>, S>* {
Spin<double, D, S>* s1 = rng.pick(M.s);
Spin<double, D, S>* s2 = rng.pick(M.s);
while (s1 == s2) {
s2 = rng.pick(M.s);
}
Vector<double, D> t1 = s1->x;
Vector<double, D> t2 = s2->x;
Vector<double, D> t12 = t1 - t2;
Vector<double, D> t = t2;
double θ =
atan2(t12(1), t12(0)) + rng.variate<double, std::normal_distribution>(0.0, ε) / t12.norm();
return new SpinFlip<double, D, Euclidean<double, D>, S>(M, flipAround(θ, t), s1);
};
}
template <int D, class S> Gen<double, D, Euclidean<double, D>, S> centerGen(double ε) {
return [ε](Model<double, D, Euclidean<double, D>, S>& M,
Rng& rng) -> Transformation<double, D, Euclidean<double, D>, S>* {
double θ = rng.uniform((double)0.0, 2 * M_PI);
Vector<double, D> t = M.s0.t;
for (unsigned j = 0; j < D; j++) {
t(j) += rng.variate<double, std::normal_distribution>(0.0, ε);
}
Spin<double, D, S>* s = rng.pick(M.s);
return new SpinFlip<double, D, Euclidean<double, D>, S>(M, flipAround(θ, t), s);
};
}
|
