Precision Bootstrap Derivation of 3D Ising Critical Exponents via Hyperscaling — E8 Intelligence Research

Abstract

FINDING: The 3D Ising model's critical exponents are now derived to unprecedented precision via the conformal bootstrap, yielding α ≈ 0.110 (from the hyperscaling relation α = 2 − 3ν, with ν ≈ 0.629971), a non-rational number that emerges from crossing symmetry and unitarity constraints rather than perturbation theory. | MATH: Hyperscaling: α = 2 − Dν (D=3). Bootstrap-derived: ν = 0.629971(4), η = 0.036298(2), Δ_σ = 0.5181489(10), Δ_ε = 1.412625(10). The exponents satisfy the scaling relations: α + 2β + γ = 2, γ = ν(2−η). Key algebraic structure: crossing equations for ⟨σσσσ⟩ and ⟨σσεε⟩ correlators, solved via semidefinite programming (SDPB) with rational approximants to the conformal block functions. | CONNECTION: The critical exponents are not simple rationals, but the bootstrap solution space is constrained by the *golden ratio-adjacent* fixed point structure: the ratio of the two relevant operator dimensions Δ_ε/Δ_σ ≈ 1.412625/0.518149 ≈ 2.726 — no direct golden ratio. However, the Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com