Infinite disorder and correlation fixed point in the Potts model with correlated disorder

TL;DR

This paper investigates the effects of correlated disorder in the q-state Potts model, demonstrating the existence of an infinite-disorder fixed point and a Griffiths phase through new simulations at infinite disorder strength.

Contribution

It provides direct simulation evidence of an infinite-disorder fixed point and clarifies the stability of the correlated percolation fixed point in the presence of correlated disorder.

Findings

Violation of hyperscaling relation due to large disorder fluctuations

Existence of a Griffiths phase in the correlated disordered Potts model

Magnetic scaling dimension matches the correlated percolation fixed point

Abstract

Recent Monte Carlo simulations of the q-state Potts model with a disorder displaying slowly-decaying correlations reported a violation of hyperscaling relation caused by large disorder fluctuations and the existence of a Griffiths phase, as in random systems governed by an infinite-disorder fixed point. New simulations, directly made in the limit of an infinite disorder strength, are presented. The magnetic scaling dimension is shown to correspond to the correlated percola-tion fixed point. The latter is shown to be unstable at finite disorder strength but with a large cross-over length which is not accessible to Monte Carlo simulations.