Recipes for metastable states in Spin Glasses

TL;DR

This paper introduces a method to analyze metastable states in spin glasses by examining a potential function related to free energy constraints, applied to spherical p-spin models, revealing a link between local minima and metastable states.

Contribution

It develops and applies a novel method to identify and study metastable states in spin glasses, connecting potential minima to metastability in the system.

Findings

Local minima of the potential correspond to metastable states.

The method confirms metastable states through relaxation dynamics.

Analysis applies between dynamic and static transition temperatures.

Abstract

In this paper we develop a method introduced by one of us to study metastable states in spin glasses. We consider a `potential function' defined as the free energy of a system at a given temperature $T$ constrained to have a fixed overlap with a reference configuration of equilibrium at temperature $T'$. We apply the method to the spherical p-spin glass and to some generalization of this model in the range of temperatures between the dynamic and the static transition. The analysis suggests a correspondence among local minima of the potential and metastable states. This correspondence is confirmed studying the relaxation dynamics at temperature $T$ of a system starting from an initial configuration equilibrated at a different temperature $T'$.