Double Criticality of the Sherrington-Kirkpatrick Model at T=0

TL;DR

This paper uses high-order numerical analysis to reveal the complex singular structure and critical points of the Sherrington-Kirkpatrick spin glass model at zero temperature, advancing understanding of its replica symmetry breaking behavior.

Contribution

It provides the first detailed numerical prediction of the singular structure and critical points of the SK model at T=0, including corrections to the order function q(a).

Findings

Confirmed single parameter scaling at T=0.

Identified two critical points at a=0 and a=∞ for infinite RSB.

Achieved unprecedented accuracy in finite-RSB scaling and energy calculations.

Abstract

Numerical results up to 42nd order of replica symmetry breaking (RSB) are used to predict the singular structure of the SK spin glass at T=0. We confirm predominant single parameter scaling and derive corrections for the T=0 order function q(a), related to a Langevin equation with pseudotime 1/a. a=0 and a=\infty are shown to be two critical points for \infty-RSB, associated with two discrete spectra of Parisi block size ratios, attached to a continuous spectrum. Finite-RSB-size scaling, associated exponents, and T=0-energy are obtained with unprecedented accuracy.