Golden-ratio algebraic structure in 2D Ising critical exponents — E8 Intelligence Research

FINDING: The 2D Ising model at criticality is a conformal field theory (c = 1/2 minimal model) whose scaling operators carry irrational exponents set by the golden-ratio-related quantity √5 — the same algebraic structure that generates φ = 1.618. MATH: - Onsager critical temperature: sinh(2J/kTc) = 1 → kTc/J = 2/ln(1+√2) ≈ 2.269 - Spontaneous magnetization exponent: β = 1/8 - Correlation length exponent: ν = 1 - Energy (thermal) exponent: α = 0 (log divergence) - Magnetic scaling dimension: Δσ = 1/8, Δε = 1 - Central charge: c = 1/2 - Kac formula for the c = 1/2 minimal model dimensions: h_{r,s} = [(r(3−p) − s·p)² − (p−3)²] / (4p(p−3)), with p = 4 (m = 3) → h_{1,1}=0, h_{1,2}=1/16, h_{2,1}=1/2, h_{2,2}=1/16, h_{1,3}=1/2, h_{3,1}=1/16 - The modular S-matrix of the c = 1/2 model has entries built from sin(π/5)-type factors; the fusion rules close on the golden-ratio ring Z[φ] (the Fibonacci-like fusion category). Specifically the Ising fusion category has quantum dimensions {1, 1, √ Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com