Further evidence of the absence of Replica Symmetry Breaking in Random Bond Potts Models

TL;DR

This paper provides strong statistical evidence supporting the replica symmetric approach in random bond q-state Potts models, challenging the applicability of replica symmetry breaking schemes in this context.

Contribution

It offers the first comprehensive numerical validation against RSB in these models using generalized scaling laws of correlation functions.

Findings

No evidence of RSB effects in Monte Carlo simulations

Numerical results align with replica symmetric predictions

RSB effects do not increase with higher moments

Abstract

In this short note, we present supporting evidence for the replica symmetric approach to the random bond q-state Potts models. The evidence is statistically strong enough to reject the applicability of the Parisi replica symmetry breaking scheme to this class of models. The test we use is a generalization of one formerly proposed by Dotsenko et al. and consists in measuring scaling laws of disordered-averaged moments of the spin-spin correlation functions. Numerical results, obtained via Monte Carlo simulations for several values of q, are shown to be in fair agreement with the replica symmetric values computed by using perturbative CFT for the second and third moments of the q=3 model. RSB effects, which should increase in strength with moment, are unobserved.