Replicon modes and stability of critical behaviour of disordered systems with respect to the continuous replica symmetry breaking

TL;DR

This paper uses a field-theory approach and two-loop RG analysis to study the stability of critical behaviour in disordered systems with replica symmetry breaking, confirming the stability of traditional fixed points even with continuous RSB modes.

Contribution

It extends previous one-step RSB RG analysis to continuous RSB modes, demonstrating the stability of fixed points in disordered critical systems.

Findings

Traditional fixed points remain stable with continuous RSB modes.

Two-loop RG analysis confirms stability of critical behaviour.

Replicon eigenvalues indicate fixed-point stability.

Abstract

A field-theory approach is used to investigate the ''spin-glass effects'' on the critical behaviour of systems with weak temperature-like quenched disorder. The renormalization group (RG) analysis of the effective Hamiltonian of a model with replica symmetry breaking (RSB) potentials of a general type is carried out in the two-loop approximation. The fixed-point (FP) stability, recently found within the one-step RSB RG treatment, is further explored in terms of replicon eigenvalues. We find that the traditional FPs, which are usually considered to describe the disorder-induced universal critical behaviour, remain stable when the continuous RSB modes are taken into account.