Critical behavior of the three-state random-field Potts model in three dimensions

TL;DR

This paper investigates the critical behavior of the three-state random-field Potts model in three dimensions, revealing evidence for a continuous phase transition and providing critical exponents through finite-size scaling analysis.

Contribution

It introduces a novel application of graph-cut methods to study the three-state random-field Potts model at zero temperature, filling a gap in understanding its phase transition behavior.

Findings

Evidence for a continuous phase transition.

Critical exponents determined via finite-size scaling.

Comparison with the random-field Ising model.

Abstract

Enormous advances have been made in the past 20 years in our understanding of the random-field Ising model, and there is now consensus on many aspects of its behavior at least in thermal equilibrium. In contrast, little is known about its generalization to the random-field Potts model which has wide-ranging applications. Here we start filling this gap with an investigation of the three-state random-field Potts model in three dimensions. Building on the success of ground-state calculations for the Ising system, we use a recently developed approximate scheme based on graph-cut methods to study the properties of the zero-temperature random fixed point of the system that determines the zero and non-zero temperature transition behavior. We find compelling evidence for a continuous phase transition. Implementing an extensive finite-size scaling (FSS) analysis, we determine the critical exponents and compare them to those of the random-field Ising model.