Large deviations in spin-glass ground-state energies

TL;DR

This paper investigates the large deviations of ground-state energies in spin glasses, revealing non-trivial scaling laws and providing semi-analytical insights, especially for the Sherrington-Kirkpatrick model.

Contribution

It introduces a detailed analysis of large deviations in spin-glass ground states, highlighting new scaling behaviors and comparing different models including the SK model.

Findings

Large deviations exhibit non-trivial N-scaling laws.

Semi-analytical results help understand hierarchical lattice models.

Comparison with Tracy-Widom distribution for the spherical approximation.

Abstract

The ground-state energy E_0 of a spin glass is an example of an extreme statistic. We consider the large deviations of this energy for a variety of models when the number of spins N goes to infinity. In most cases, the behavior can be understood qualitatively, in particular with the help of semi-analytical results for hierarchical lattices. Particular attention is paid to the Sherrington-Kirkpatrick model; after comparing to the Tracy-Widom distribution which follows from the spherical approximation, we find that the large deviations give rise to non-trivial scaling laws with N.