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

Abstract

Enormous advances have been made in the past 20 years in our understanding of the random-field Ising model (RFIM), 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 (RFPM) which has wide-ranging applications. Here, we start filling this gap with an investigation of the three-state RFPM 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 nonzero temperature transition behavior. We find compelling evidence for a continuous phase transition. Implementing an extensive finite-size scaling analysis, we determine the critical exponents and compare them to those of the RFIM.