Cavity Method for Supersymmetry Breaking Spin Glasses

TL;DR

This paper develops a generalized cavity method to analyze supersymmetry-breaking in spin glasses, specifically applying it to the Sherrington-Kirkpatrick model to accurately compute local magnetization distributions.

Contribution

It introduces a new cavity approach that handles supersymmetry-breaking, extending the standard method to systems with marginal modes and metastable state fragility.

Findings

Method accurately reproduces supersymmetry-breaking results

Applied to Sherrington-Kirkpatrick model

Matches theoretical predictions for local magnetizations

Abstract

The spontaneous supersymmetry-breaking that takes place in certain spin-glass models signals a particular fragility in the structure of metastable states of such systems. This fragility is due to the presence of at least one marginal mode in the Hessian of the free energy, that makes the states highly susceptible under external perturbations. The cavity method is a technique that recursively describes the property of a system with N+1 spins in terms of those of a system with N spins. To do so, the cavity method assumes a certain degree of stability when adding a new spin to the system, i.e. it assumes that for a generic choice of the parameters there is an one-to-one correspondence between the metastable states of the system with N spins and the metastable states of the system with N+1 spins. In systems where the supersymmetry is broken such a correspondence does not exist, and an alternative formulation of the cavity method must be devised. We introduce a generalized cavity approach that takes care of this problem and we apply it to the computation of the probability distribution of the local magnetizations in the Sherrington-Kirkpatrick model. Our findings agree with the correct supersymmetry-breaking result.