Griffiths phase and critical behavior of the 2D Potts models with long-range correlated disorder

TL;DR

This study investigates the 2D Potts model with long-range correlated disorder, revealing a Griffiths phase with algebraic finite-size scaling and critical exponents influenced by disorder correlations, not the number of states.

Contribution

It provides the first large-scale Monte Carlo evidence of a Griffiths phase in the 2D Potts model with long-range correlated disorder and analyzes its critical behavior.

Findings

Existence of a Griffiths phase with algebraic finite-size scaling.

Critical exponents depend on disorder correlation decay, not on the number of states.

Violation of hyperscaling relations across the Griffiths phase.

Abstract

The $q$-state Potts model with a long-range correlated disorder is studied by means of large-scale Monte Carlo simulations for $q=2,4,8$ and 16. Evidence is given of the existence of a Griffiths phase, where the thermodynamic quantities display an algebraic Finite-Size Scaling, in a finite range of temperatures around the self-dual point. The critical exponents are shown to depend on both the temperature and the exponent of the algebraic decay of disorder correlations, but not on the number of states of the Potts model. The mechanism leading to the violation of hyperscaling relations is observed in the entire Griffiths phase.