Absence of φ² Exponent in Disordered Quantum Phase Transitions — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: The search results are a scattered set of lecture videos and papers on quantum phase transitions, topological defects, and critical exponents — no direct evidence of φ² (2.618) appearing as a correlation-length exponent in any disordered quantum phase transition. The closest mathematical anchor is the 2D XY model's Kosterlitz-Thouless (KT) transition, where correlation length diverges exponentially, not as a power law. MATH: - KT transition: ξ ~ exp(b / √|T − T_KT|) — no power-law exponent, hence no φ². - Standard correlation-length exponent ν ≈ 0.6717 (3D Ising), ν = 1 (mean field), ν = 2/3 (2D Ising) — none equal 2.618. - The hard-sphere phase shift example (MIT 8.06) involves scattering phase shifts δ_l, not critical exponents. - The driven XY ferromagnet paper (arXiv:1706.01619) studies non-equilibrium phase transitions via Monte Carlo — no reported φ² ratio. CONNECTION: - The 2D XY model has U(1) symmetry and vortex-antivortex unbinding — topological, not geometric-ha Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204220956
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