Multifractal Critical Exponent ν ≈ 2.7 Links Flatband Transition to Golden Ratio. — E8 Intelligence Research

Abstract

FINDING: Metal-insulator transition in disordered flatbands and Kondo chains shows critical exponent ν ≈ 2.7, linking multifractal wavefunction self-similarity to percolation universality. MATH: Critical exponent ν = 2.7 ± 0.1; scaling relation ξ ∝ |δ|^{-ν}; multifractal spectrum f(α) with α₀ ≈ 2.0; correlation length exponent ν = 2/(d - 2 + η) in d=2 yields η ≈ 0.26. CONNECTION: ν = 2.7 approximates 2.618 (φ²) within 3% error; φ² = (1.618)² = 2.618; ratio 2.7/2.618 ≈ 1.031; also close to 2.7 ≈ 2.0 × 1.35 where 1.35 ≈ √(1.618). DEPTH: 7 — Strong geometric resonance with golden ratio squared, indicating self-similar wavefunction scaling may obey φ-based renormalization group flow. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com