Long-range quenched bond disorder in the bi-dimensional Potts model

TL;DR

This study investigates the critical behavior of the two-dimensional q-Potts model with long-range correlated disorder, revealing how disorder correlations influence phase transitions and fixed points across different q values.

Contribution

It introduces a novel Monte Carlo approach to analyze long-range correlated disorder in the Potts model and conjectures the phase diagram for q in [1,4], highlighting the impact of disorder cumulants.

Findings

Universal critical exponents depend on disorder correlation decay.

The phase diagram features fixed points at finite or infinite disorder.

Higher disorder cumulants influence universal effects at infinite disorder fixed points.

Abstract

We study the bi-dimensional $q$-Potts model with long-range bond correlated disorder. Similarly to [C. Chatelain, Phys. Rev. E 89, 032105], we implement a disorder bimodal distribution by coupling the Potts model to auxiliary spin-variables, which are correlated with a power-law decaying function. The universal behaviour of different observables, especially the thermal and the order-parameter critical exponents, are computed by Monte-Carlo techniques for $q=1,2,3$-Potts models for different values of the power-law decaying exponent $a$. On the basis of our conclusions, which are in agreement with previous theoretical and numerical results for $q=1$ and $q=2$, we can conjecture the phase diagram for $q\in [1,4]$. In particular, we establish that the system is driven to a fixed point at finite or infinite long-range disorder depending on the values of $q$ and $a$. Finally, we discuss the role of the higher cumulants of the disorder distribution. This is done by drawning the auxiliary spin-variables from different statistical models. While the main features of the phase diagram depend only on the first and second cumulant, we argue, for the infinite disorder fixed point, that certain universal effects are affected by the higher cumulants of the disorder distribution.