Antiferromagnetic Potts models on the square lattice

We study the antiferromagnetic q-state Potts model on the square lattice for q=3 and 4, using the Wang-Swendsen-Kotecký Monte Carlo algorithm and a finite-size-scaling extrapolation method. For q=3, we obtain good control up to correlation length ξ∼5000; the data are consistent with ξ(β)=Ae2ββ(1+a1e-β+...) as β→. For q=4, the model is disordered even at zero temperature.