Sj. Ferreira et Ad. Sokal, Antiferromagnetic potts models on the square lattice: A high-precision Monte Carlo study, J STAT PHYS, 96(3-4), 1999, pp. 461-530
study the antiferromagnetic q-state Potts model on the square lattice for q
= 3 and q = 4, using the Wang-Swendsen-Kotecky (WSK) Monte Carlo algorithm
and a powerful finite-size-scaling extrapolation method. For q=3 we obtain
good control up to correlation length xi similar to 5000; the data are con
sistent with xi(B)=Ae(2 beta)beta(P)(1 + a(1)e(-beta) + ...) as beta--> inf
inity, with p approximate to 1. The staggered susceptibility behaves as chi
(stagg) similar to xi(5/3). For q = 4 the model is disordered (xi less than
or similar to 2) even at zero temperature. In appendices we prove a correl
ation inequality for Potts antiferromagnets on a bipartite lattice, and we
prove ergodicity of the WSK algorithm at zero temperature for Potts antifer
romagnets on a bipartite lattice.