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
//! Ising-model constructions and the exact results the sampler must reproduce before it is
//! trusted with anything else: exact Boltzmann enumeration for small systems, and Onsager's
//! spontaneous magnetization for the 2D nearest-neighbor lattice (Onsager 1944 / Yang 1952):
//! M(beta) = (1 - sinh(2 beta J)^-4)^(1/8) for beta > beta_c = ln(1+sqrt(2))/2 ~ 0.4407,
//! M = 0 above.
use crate::graph::{Graph, GraphBuilder};
/// Ring of n spins, uniform coupling j, per-site bias h.
pub fn ring(n: usize, j: f64, h: f64) -> Graph {
let mut gb = GraphBuilder::new(n);
for i in 0..n {
gb.couple(i, (i + 1) % n, j);
if h != 0.0 {
gb.bias(i, h);
}
}
gb.build()
}
/// 2D nearest-neighbor square lattice with periodic boundaries, uniform J, no field.
pub fn lattice2d(l: usize, j: f64) -> Graph {
// A side of 1 wraps every neighbour onto the site itself, so the periodic boundary produces the
// self-edge (0,0), which `GraphBuilder::couple` refuses with a panic -- reached through
// `ft_ising2d_new(1, ..)` that is a NON-UNWINDING panic and aborts the caller's process, while
// the header documents a NULL return. `l = 0` already returned a live empty handle, so the
// guard band stopped one short of the fatal value. An uncoupled lattice is the honest answer
// for a side with no distinct neighbours.
if l < 2 {
return GraphBuilder::new(l * l).build();
}
let mut gb = GraphBuilder::new(l * l);
for y in 0..l {
for x in 0..l {
let i = y * l + x;
gb.couple(i, y * l + (x + 1) % l, j);
gb.couple(i, ((y + 1) % l) * l + x, j);
}
}
gb.build()
}
/// Exact Boltzmann distribution over all 2^n states (n <= 24). Returns probabilities indexed by
/// bitmask (bit b set => spin b = +1).
pub fn exact_boltzmann(g: &Graph, beta: f64) -> Vec<f64> {
assert!(g.n <= 24, "exact enumeration limited to 24 spins");
let m = 1usize << g.n;
let mut p = vec![0.0f64; m];
let mut s = vec![-1i8; g.n];
// Two passes with a max shift, because `exp(-beta*E)` overflows long before beta gets large.
//
// This used to accumulate `(-beta * g.energy(&s)).exp()` directly. `f64` tops out near
// exp(709), so on a 24-spin complete ferromagnet (E_min = -276) beta = 3 already overflows two
// states to +inf, z becomes inf, and every p = w/inf comes back 0 or NaN. The crate's OWN
// schedules run to beta 6 and 8, and this is the exact reference every sampler is verified
// against -- so the oracle silently stopped answering inside the range it is used in, and
// `certify` swallowed it because `NaN > floor` is false.
//
// Subtracting the maximum log-weight leaves the normalised distribution identical (the shift
// cancels in w/z) and keeps every exponent at or below zero. `HetSampler::sweep` already did
// exactly this; the enumerations simply never got it.
let mut mx = f64::NEG_INFINITY;
for mask in 0..m {
for b in 0..g.n {
s[b] = if mask >> b & 1 == 1 { 1 } else { -1 };
}
let l = -beta * g.energy(&s);
p[mask] = l;
if l > mx {
mx = l;
}
}
let mut z = 0.0;
for v in p.iter_mut() {
*v = (*v - mx).exp();
z += *v;
}
for v in p.iter_mut() {
*v /= z;
}
p
}
/// Onsager/Yang exact spontaneous magnetization for the infinite 2D lattice (J=1).
pub fn onsager_m(beta: f64) -> f64 {
let s = (2.0 * beta).sinh();
let x = 1.0 - s.powi(-4);
if x <= 0.0 {
0.0
} else {
x.powf(1.0 / 8.0)
}
}
/// Total-variation distance between two distributions.
pub fn tv(p: &[f64], q: &[f64]) -> f64 {
// `zip` stops at the shorter of the two, so mismatched lengths used to return a TRUNCATED
// distance rather than an error: `tv(&[0.25; 4], &[0.5, 0.5])` gave 0.25 where the honest
// answer over the shared 4-state space is 0.5. Truncation always under-estimates, and every
// use of this function has the shape `assert!(tv < tolerance)` -- so the failure direction was
// the one that turns a red test green.
assert_eq!(
p.len(),
q.len(),
"total variation needs two distributions over the SAME state space"
);
p.iter().zip(q).map(|(a, b)| (a - b).abs()).sum::<f64>() / 2.0
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn the_exact_reference_survives_the_betas_its_own_schedules_use() {
// This is the oracle every sampler in the crate is verified against, and it used to return
// NaN. `exp(-beta*E)` overflows f64 near exp(709), so a large beta sent z to +inf and every
// p to 0 or NaN -- and `certify` swallowed it, because `NaN > floor` is false. The crate's
// own schedules run to beta 6 and 8, so this was inside the range it is actually used in.
let g = ring(8, 1.0, 0.0);
for beta in [1.0, 3.0, 6.0, 8.0, 24.0, 200.0] {
let p = exact_boltzmann(&g, beta);
assert!(p.iter().all(|v| v.is_finite()), "beta={beta} produced a non-finite entry");
let sum: f64 = p.iter().sum();
assert!((sum - 1.0).abs() < 1e-12, "beta={beta} sums to {sum}, not 1");
}
// Still RIGHT, not merely finite: at low temperature a ferromagnetic ring puts half its
// mass on all-down and half on all-up, and nothing measurable anywhere else.
let p = exact_boltzmann(&g, 20.0);
assert!((p[0] - 0.5).abs() < 1e-9, "all-down should carry half the mass, got {}", p[0]);
assert!((p[255] - 0.5).abs() < 1e-9, "all-up should carry half the mass, got {}", p[255]);
}
#[test]
#[should_panic(expected = "SAME state space")]
fn a_total_variation_between_different_sized_distributions_is_refused() {
// `zip` stopped at the shorter one, so this returned 0.25 where the honest answer over the
// shared 4-state space is 0.5. Truncation always UNDER-estimates, and every use of `tv` has
// the shape `assert!(tv < tolerance)` -- the failure direction that turns a red test green.
let _ = tv(&[0.25, 0.25, 0.25, 0.25], &[0.5, 0.5]);
}
}