FRSB in the SK spin glass: convergence to full-interval support at zero temperature

Hong-Bin Chen

arXiv:2607.18032v1 Primary: math.PR Secondary: cond-mat.dis-nn, math-ph

Abstract

We prove full replica symmetry breaking for the zero-field Sherrington-Kirkpatrick model at zero temperature: the Parisi minimizer is absolutely continuous, has a smooth density, and has support $[0,1)$. At inverse temperature $β>1$, [arxiv.org/abs/2607.11756v3] recently proved that the Parisi measure has support $[0,q_β]$. Here, we show $q_β$ converges to $1$ as $β\to\infty$.

Disclosure

“40 pages: 25 main text, 15 appendices/references. Successor to an AI-generated aiXiv preprint. ChatGPT 5.6 is the actual author: it generated the proof arguments and prose. Hong-Bin Chen is formally listed as author only to comply with arXiv policy and accepts full responsibility. A conditional Lean 4 formalization machine-checks Theorems 1”
arXiv metadata: comment

Classification: Substantial proof generation
Multiplier: 10
Verified: 2026-08-23T18:59:07.241946Z

Structural counts

Pages 40 pdf

Theorems 3 source

Lemmas 12 source

Propositions 13 source

Corollaries 0 source

Definitions 0 source

Displayed equations 393 source

Bibliography entries 20 source

Appendix pages 40 estimated

Count notes

Source counts use the expanded primary TeX file main.tex.
Appendix pages include the first PDF page with an explicit Appendix heading through the final page.