Saddle Points Stability in the Replica Approach Off Equilibrium

TL;DR

This paper investigates the stability of saddle points in the replica free energy landscape of a spin glass model near the glass transition, revealing insights into metastable states through stability analysis of constrained replicas.

Contribution

It introduces a stability analysis method for metastable saddle points in the replica approach, providing new interpretation of their role in spin glass models.

Findings

Identification of non-trivial metastable saddle points near the glass transition

Interpretation of saddle points through stability analysis of constrained replicas

Insights into the complex free energy landscape of spin glasses

Abstract

We study the replica free energy surface for a spin glass model near the glassy temperature. In this model the simplicity of the equilibrium solution hides non trivial metastable saddle points. By means of the stability analysis performed for one and two real replicas constrained, an interpretation for some of them is achieved.