Barriers in the p-spin interacting spin-glass model. The dynamical approach

TL;DR

This paper studies energy barriers between metastable states in the spherical p-spin glass model using instanton methods, revealing how to compute barrier heights and escape probabilities.

Contribution

It introduces a causal two-real-replica dynamics approach to determine barrier heights and escape probabilities in the p-spin glass model.

Findings

Derived the probability of escaping high-energy metastable states.

Calculated the energy barriers associated with escape processes.

Reduced barrier height calculation to a causal two-replica dynamics problem.

Abstract

We investigate the barriers separating metastable states in the spherical p-spin glass model using the instanton method. We show that the problem of finding the barrier heights can be reduced to the causal two-real-replica dynamics. We find the probability for the system to escape one of the highest energy metastable states and the energy barrier corresponding to this process.