Stability of a two-sublattice spin-glass model

TL;DR

This paper analyzes the stability of the replica-symmetric solution in a two-sublattice spin-glass model, providing generalized conditions for phase diagram analysis using the Hurwitz criterion.

Contribution

It introduces a generalized stability condition for complex eigenvalues in a two-sublattice spin-glass model, enabling more accurate phase diagram analysis.

Findings

Eigenvalues associated with perturbations are generally complex.

The Hurwitz criterion is used to determine stability.

The stability condition facilitates phase diagram analysis.

Abstract

We study the stability of the replica-symmetric solution of a two-sublattice infinite-range spin-glass model, which can describe the transition from antiferromagnetic to spin glass state. The eigenvalues associated with replica-symmetric perturbations are in general complex. The natural generalization of the usual stability condition is to require the real part of these eigenvalues to be positive. The necessary and sufficient conditions for all the roots of the secular equation to have positive real parts is given by the Hurwitz criterion. The generalized stability condition allows a consistent analysis of the phase diagram within the replica-symmetric approximation.