Disorder-Driven Metal-Insulator Transition in Topological Insulators with Critical Exponent ν ≈ 2.7 — E8 Intelligence Research

Abstract

FINDING: Topological insulators exhibit a metal-insulator transition with critical exponent ν ≈ 2.7, driven by disorder, linking to universal scaling behavior. | MATH: Critical exponent ν ~ 2.7 from scaling analysis of localization length; no deviation from metal-ordinary insulator transitions in systems of orthogonal symmetry class. | CONNECTION: No direct geometric harmony ratios (0.382, 0.618, etc.) or base-60 links; however, the critical exponent ν ~ 2.7 is near 2.618 (φ², where φ = 1.618), suggesting a possible resonance with golden ratio scaling in critical phenomena. Lattice structure implicit in topological band theory (e.g., honeycomb, square lattices) but not specified in findings. | DEPTH: 6 — The critical exponent is a precise mathematical constant from scaling theory, but the connection to geometric harmony is speculative; the finding advances understanding of universality classes in disordered topological phases, not fundamental geometric structure. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com