Structure of metastable states in spin glasses by means of a three replica potential

TL;DR

This paper introduces a three replica potential to analyze the structure of metastable states in the spherical p-spin model, providing insights into the system's dynamics and the distribution of equilibrium states.

Contribution

It presents a novel three replica potential method to study metastable states and their organization in phase space above the static transition temperature.

Findings

Identifies the distance between equilibrium and local states.

Reveals non-random distribution of equilibrium states.

Provides information on system dynamics near the transition.

Abstract

We introduce a three replica potential useful to examine the structure of metastables states above the static transition temperature, in the spherical p-spin model. Studying the minima of the potential we are able to find which is the distance between the nearest equilibrium and local equilibrium states, obtaining in this way information on the dynamics of the system. Furthermore, the analysis of the potential at the dynamical transition temperature suggests that equilibrium states are not randomly distributed in the phase space.