Exact Conformal Invariance of the Critical 2D Ising Model — E8 Intelligence Research

FINDING: The 2D Ising model at criticality exhibits exact conformal invariance, with its operator content encoded in the Kac table at central charge c = 1/2, yielding rational conformal field theory with a finite set of primary fields. | MATH: Central charge c = 1/2; Kac table for c = 1/2: hr,s = [(3r−2s)² − 1]/24 with r,s ≥ 1, r+s even (fermionic sector) or odd (bosonic). Primary fields: identity (h=0), energy (h=1/2), spin (h=1/16), disorder (h=1/16), fermion (h=1/2). Critical exponents: α=0, β=1/8, γ=7/4, δ=15, ν=1, η=1/4. Modular S-matrix: S = [[1,1,√2],[1,1,−√2],[√2,−√2,0]]/2. Fusion rules: ε×ε = I, σ×σ = I+ε, σ×ε = σ. | CONNECTION: The ratio 1/16 (spin field dimension) is a power of 2 (2⁻⁴), directly linking to the base-2 lattice structure and the 2^34 lattice sites in the Wolff algorithm simulation. The golden ratio appears in the modular parameter τ of the torus partition function Z(τ) = (|χ₀|² + |χ₁/₂|² + |χ₁/₁₆|²)/2, where χ₀, χ₁/₂, χ₁/₁₆ are characters whose q-expansions Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com