Role of the Tracy-Widom distribution in the finite-size fluctuations of the critical temperature of the Sherrington-Kirkpatrick spin glass

TL;DR

This paper analyzes how the critical temperature fluctuations in the Sherrington-Kirkpatrick spin glass are governed by the Tracy-Widom distribution, using finite-size spectral analysis and random matrix theory.

Contribution

It demonstrates that the finite-size fluctuations of the critical temperature follow the Tracy-Widom distribution with a 2/3 scaling exponent, linking spin glass physics to random matrix theory.

Findings

Critical temperature fluctuations follow Tracy-Widom distribution

Finite-size scaling exponent is 2/3

Spectral analysis of susceptibility matrix reveals key insights

Abstract

We investigate the finite-size fluctuations due to quenched disorder of the critical temperature of the Sherrington-Kirkpatrick spin glass. In order to accomplish this task, we perform a finite-size analysis of the spectrum of the susceptibility matrix obtained via the Plefka expansion. By exploiting results from random matrix theory, we obtain that the fluctuations of the critical temperature are described by the Tracy-Widom distribution with a non-trivial scaling exponent 2/3.