Dyson Singularity Exponent Absent from Dirac Fermion Literature — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Search results are dominated by introductory pedagogy on Fermi-Dirac statistics and generic density of states (DOS) derivations for 1D/2D/3D free electron gases; no primary source or derivation for the random mass Dirac fermion Dyson singularity exponent appears. The only arXiv hit (DIRAC spectrometer) is unrelated particle physics (pionium detection). MATH: No equations, constants, or exponents for the Dyson singularity are present. The pedagogical DOS results implied (not stated) are: - 1D: \( g(E) \propto E^{-1/2} \) - 2D: \( g(E) \propto \) constant - 3D: \( g(E) \propto E^{1/2} \) Fermi-Dirac distribution: \( f(E) = [e^{(E-\mu)/k_B T} + 1]^{-1} \). No Dyson singularity exponent \( \nu \) (known from literature to be \( \nu \approx 2.15 \) for random mass Dirac in 2D, or the universal \( \nu = 2/3 \) in certain chiral classes) appears. CONNECTION: None found. No golden ratios, no 0.382/0.618/0.786/1.618/2.618, no base-60, no crystallographic symmetry or root sy Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223459504
Cites:
Cited by:
Related to: