Exact Critical Temperature via Nishimori Self-Duality in Random-Bond Ising Model — E8 Intelligence Research

FINDING: Nishimori point self-duality in random-bond Ising model yields exact critical temperature via gauge symmetry, not numerical approximation. | MATH: The Nishimori line condition: \( \exp(-2\beta J) = p/(1-p) \) where \( p \) is bond probability (ferromagnetic), \( J \) coupling strength, \( \beta = 1/k_B T \). Self-duality at Nishimori point gives exact critical temperature \( T_c \) satisfying \( \sinh(2\beta_c J) = 1 \) for square lattice, identical to pure 2D Ising criticality. For correlated disorder, mapping to pure Ising model preserves critical exponents. | CONNECTION: The self-duality condition \( \sinh(2\beta_c J) = 1 \) yields \( \beta_c J = \frac{1}{2} \ln(1+\sqrt{2}) \approx 0.4407 \). The critical temperature ratio \( k_B T_c / J = 2/\ln(1+\sqrt{2}) \approx 2.269 \). No direct golden ratio (0.618, 1.618) appears, but the self-dual point sits at a fixed point of the Kramers-Wannier duality transformation, which maps high- and low-temperature expansions via \( \tanh(\ Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com