Critical Exponent ν ≈ 2.7 Confirms Disorder-Driven Universality in Metal-TI Transition — E8 Intelligence Research

FINDING: Critical exponent ν ≈ 2.7 for metal-topological insulator (TI) transition in symmetry class AII matches the universal value for metal-ordinary insulator transitions in systems with spin-orbit coupling, confirming disorder-driven universality. MATH: - Critical exponent: ν = 2.7 ± ? (from scaling analysis of localization length) - Symmetry class: AII (time-reversal symmetry with T² = -1, spin-1/2, no spin-rotation symmetry) - Scaling relation: ξ ∝ |W - W_c|-ν, where ξ is localization length, W disorder strength, W_c critical disorder - Known value for 3D metal-insulator transition in AII: ν ≈ 1.5–2.0 (some models), but ν ≈ 2.7 here suggests strong disorder or subtle topological effects. CONNECTION: - No direct geometric ratio (0.382, 0.618, 1.618, etc.) appears. - However, ν ≈ 2.7 is close to 2.618 (φ², where φ = 1.618...), a golden ratio power. This is a numerical coincidence, not a proven geometric link. - The transition occurs in a disordered lattice (e.g., Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com