Vertex weights are conditional probabilities, so a configuration is
generated in one sweep: exact, O(N²), no Markov chain and no
mixing time. Δ = (b₁+b₂)/(2√(b₁b₂))
≥ 1 by AM–GM, so this covers the ferroelectric regime,
which is the hardest one under DWBC.
Exact sampling by CFTP needs c1c2 ≥
a1a2 and c1c2 ≥
b1b2. Outside that region no monotone
coupling of the update exists, so no CFTP scheme is valid there.
Raise the c weights, or lower a and b, to re-enable it.
parameters
|Δ|>1 (ferroelectric/antiferroelectric): local Monte Carlo dynamics genuinely mix very slowly
here (this is known physics, not a bug) -- Run will likely look visually
"stuck", and successive frames stay correlated for a long time.
Exact Sample sidesteps mixing entirely and is correct in this regime, but
only up to the size limit noted below: reaching |Δ|>1 requires non-uniform weights,
where the exact method's cost grows exponentially with n. Above that limit no exact method
is available and the button is disabled.
export
sweeps elapsed: 0
a1=a2=1 fixed (WLOG by gauge freedom -- the
model only depends on 2 independent ratios). Δ>1:
ferroelectric. −1≤Δ<1: disordered. Δ<−1:
antiferroelectric. Exact sample is a mathematically
exact draw: the sequential transfer-matrix sampler for
n ≤ 14 at any weights, and Coupling From The Past
(n ≤ 250) wherever c1c2 dominates
a1a2 and b1b2. That
region contains the whole antiferroelectric phase Δ<−1,
so Δ=−3 is exactly samplable.