  We 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 $\xi \sim 5000$; the data are consistent with
$\xi(\beta) = A e^{2\beta} \beta^p (1 + a_1 e^{-\beta} + ...)$ as
$\beta\to\infty$, with $p \approx 1$. The staggered susceptibility behaves as
$\chi_{stagg} \sim \xi^{5/3}$. For q=4 the model is disordered ($\xi \ltapprox
2$) even at zero temperature. In appendices we prove a correlation inequality
for Potts antiferromagnets on a bipartite lattice, and we prove ergodicity of
the WSK algorithm at zero temperature for Potts antiferromagnets on a bipartite
lattice.
