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

FINDING: Nishimori point self-duality in the random bond Ising model yields an exact critical temperature via a symmetry line where quenched disorder averages simplify. MATH: - Nishimori condition: \( (2β J) = exp(-2β h) \) for random bond Ising model with binary disorder \( J = ± J_0 \) and uniform field \( h \). - Self-duality at the Nishimori line gives exact critical temperature \( T_c \) satisfying: \( (2β_c J_0) = 1 \) → \( β_c J_0 = 1/2 ln(1+√2) ≈ 0.4407 \). - Critical inverse temperature for pure 2D Ising: \( β_c J = 1/2 ln(1+√2) \) (Onsager). - The Nishimori point is a multicritical point where the Nishimori line meets the ferromagnetic–paramagnetic phase boundary. CONNECTION: - The critical coupling \( β_c J_0 = 0.4407 \) yields ratio \( exp(-2β_c J_0) = √2 - 1 ≈ 0.4142 \), close to the silver ratio \( √2 - 1 ≈ 0.4142 \), not the golden ratio directly. - The sel Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com