Ordering and Phase Transitions in Antiferromagnetic Potts Models

Abstract

Monte Carlo simulations and $\ensuremath{\epsilon}$ expansion techniques are used to analyze the behavior of antiferromagnetic Potts models and the Ashkin-Teller model. The Monte Carlo data show that the three- and four-state antiferromagnetic Potts models have an ordered low-temperature phase in three dimensions. Evidence is presented for the existence of a novel low-temperature, metastable, glassy "plastic crystal" phase in the four-state antiferromagnetic Potts model in three dimensions.