Absence of Direct Link Between Ising Criticality and Teichmüller Dynamics — E8 Intelligence Research

Abstract

FINDING: Mean-field Ising critical exponent β=1/2 is a classical result; the search results confirm its pedagogical ubiquity but reveal no direct link to Teichmüller dynamics or ergodic moduli-space theory — the only moduli-space paper (arXiv:2504.00931) concerns algebraic symplectic structures on framed connections, unrelated to Ising criticality. | MATH: Mean-field Ising: β = 1/2 (order parameter m ~ (T_c − T)^β), γ = 1 (susceptibility), ν = 1/2 (correlation length). 2D exact Ising: β = 1/8, γ = 7/4, ν = 1. The Wolff algorithm on 2^34 sites confirms scale invariance at criticality — fractal dimension d_f = 2 − β/ν = 2 − (1/8)/1 = 15/8 = 1.875. | CONNECTION: The 2D Ising critical point exhibits conformal invariance (central charge c = 1/2), whose operator algebra relates to the golden ratio via modular equations: the critical temperature satisfies sinh(2β_c J) = 1, giving β_c J = ln(1+√2)/2 ≈ 0.4407 — not a golden-ratio constant. However, the ratio β/ν = 1/8 = 0.125, and the combinati Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com