Antiferromagnetic Potts Models on the Square Lattice

Abstract

We study the antiferromagnetic $q$-state Potts model on the square lattice for $q=3$ and $q=4$, using the Wang-Swendsen-Kotecký Monte Carlo algorithm and a new finite-size-scaling extrapolation method. For $q=3$ we obtain good control up to correlation length $ξ\sim 5000$; the data are consistent with $ξ(β) = A e^{2β} β(1 + a_1 e^{-β} + \ldots)$ as $β\to\infty$. For $q=4$ the model is disordered even at zero temperature.