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

TL;DR

This study investigates the stability of the Griffiths phase in the 2D Potts model with correlated disorder, showing it persists in the thermodynamic limit and is influenced by disorder strength and correlation decay.

Contribution

It demonstrates that the Griffiths phase remains stable in large systems and is not just due to local transition fluctuations, highlighting the role of disorder correlations.

Findings

Griffiths phase persists in large 2D Potts systems.

Width of the Griffiths phase depends on disorder strength.

No crossover to standard critical behavior for slowly decaying correlations.

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.