Stability of the Griffiths phase in a 2D Potts model with correlated disorder

Chatelain Chatelain

doi:10.5488/cmp.17.33601

Abstract

A Griffiths phase has recently been observed by Monte Carlo simulations in the 2D $q$-state Potts model with strongly correlated quenched random couplings. In particular, the magnetic susceptibility was shown to diverge algebraically with the lattice size in a broad range of temperatures. However, only relatively small lattice sizes could be considered so one can wonder whether this Griffiths phase will not shrink and collapse into a single point, the critical point, as the lattice size is increased to much larger values. In this paper, the 2D eight-state Potts model is numerically studied for four different disorder correlations. It is shown that the Griffiths phase cannot be explained as a simple spreading of local transition temperatures caused by disorder fluctuations. As a consequence, the vanishing of the latter in the thermodynamic limit does not necessarily imply the collapse of the Griffiths phase into a single point. In contrast, the width of the Griffiths phase is controlled by the disorder strength. However, for disorder correlations decaying slower than $1/r$, no cross-over to a more usual critical behavior could be observed as this strength is tuned to weaker values.

Highlights

The effect of disorder on phase transitions and critical phenomena has attracted a considerable interest in the last decades
We recently studied the effect of correlated couplings on the 2D Potts model [10, 11] using large-scale Monte Carlo simulations
More intriguing is the fact that the phase diagram displays a Griffiths phase, as in the McCoy-Wu model, where the magnetic susceptibility diverges with the lattice size

Summary

Chatelain

Groupe de Physique Statistique, Département P2M, Institut Jean Lamour, CNRS (UMR 7198), Université de Lorraine, France. A Griffiths phase has recently been observed by Monte Carlo simulations in the 2D q-state Potts model with strongly correlated quenched random couplings. Only relatively small lattice sizes could be considered, so one can wonder whether this Griffiths phase will not shrink and collapse into a single point, the critical point, as the lattice size is increased to much larger values. It is shown that the Griffiths phase cannot be explained as a simple spreading of local transition temperatures caused by disorder fluctuations. The width of the Griffiths phase is controlled by the disorder strength. For disorder correlations decaying slower than 1/r , no cross-over to a more usual critical behavior could be observed as this strength is tuned to weaker values

Introduction

Models and simulation

Griffiths phase and disorder fluctuations

Griffiths phase and disorder strength

Conclusions