Numerical study of metastable states in Ising spin glasses

TL;DR

This paper numerically investigates the metastable states in the Sherrington-Kirkpatrick spin glass, revealing their organization into pairs and supporting the spontaneous breaking of supersymmetry in the model.

Contribution

It provides a numerical analysis of the structure of metastable states, confirming theoretical predictions about their pairing and supersymmetry breaking.

Findings

Metastable states form pairs of minima and saddle points.

Pairs coalesce in the thermodynamic limit.

Results support supersymmetry breaking in the model.

Abstract

We study numerically the structure of metastable states in the Sherrington-Kirkpatrick spin glass. We find that all non-paramagnetic stationary points of the free energy are organized into pairs, consisting in a minimum and a saddle of order one, which coalesce in the thermodynamic limit. Within the annealed approximation, the entropic contribution of these states, that is the complexity, is compatible with the supersymmetry-breaking calculation performed in [A.J. Bray and M.A. Moore, J. Phys. C, 13 L469 (1980)]. This result indicates that the supersymmetry is spontaneously broken in the Sherrington-Kirkpatrick model.