Critical behaviour of anisotropic magnets with quenched disorder: replica symmetry breaking studied by operator product expansion

TL;DR

This paper investigates the critical behavior of anisotropic disordered magnets near four dimensions, employing the replica method and operator product expansion to derive renormalization group equations with potential replica symmetry breaking.

Contribution

It introduces a first-order epsilon expansion analysis of disordered anisotropic magnets considering replica symmetry breaking effects.

Findings

Derived RG equations including replica symmetry breaking

Analyzed critical behavior near four dimensions

Provided theoretical framework for disordered anisotropic magnets

Abstract

We study critical behaviour of disordered magnets near four dimensions. We consider the system with explicit cubic anisotropy and scalar disorder and that with random direction of anisotropy axis. The quenched disorder is taken into account by replica method. Using the method of operator product expansion, we derive in the first order to $\epsilon$ approximation the renormalization group equations taking into account possible replica symmetry breaking.