Replica symmetry breaking for anisotropic magnets with quenched disorder

TL;DR

This paper investigates the critical behavior of anisotropic magnets with quenched disorder using the replica method, analyzing the stability of replica symmetric fixed points and the effects of replica symmetry breaking.

Contribution

It derives first-order epsilon expansion renormalization group equations considering replica symmetry breaking in anisotropic disordered magnets.

Findings

Replica symmetric fixed points are stable against replica symmetry breaking perturbations.

Replica symmetry breaking does not destabilize the stable fixed points.

The study provides insights into the critical behavior of disordered anisotropic magnetic systems.

Abstract

We study critical behaviour of a magnet with cubic anisotropy and quenched scalar disorder which is taken into account by replica method. We derive to first order in $\epsilon$ approximation the renormalization group equations taking into account possible replica symmetry breaking. We study the stability of the replica symmetric fixed points with respect to perturbations without (in general case) replica symmetry. However, we find that if a fixed point is stable with respect to replica symmetric deviations, it is also stable with respect to deviations without replica symmetry.