A generalised version of the interface method of Muller-Hartmann and Zittartz (1977) is applied to the three-state square lattice Potts antiferromagnet in a negative field. The phase boundary is found to go to zero temperature in the limit of zero magnetic field.
We study the antiferromagnetic q-state Potts model on the square lattice for q=3 and 4, using the Wang-Swendsen-Koteck\'y Monte Carlo algorithm and a finite-size-scaling extrapolation method. For q=3, we obtain good control up to correlation length \ensuremath{\xi}\ensuremath{\sim}5000; the data are consistent with \ensuremath{\xi}(\ensuremath{\beta})=${\mathit{Ae}}^{2\mathrm{\ensuremath{\beta}}}$\ensuremath{\beta}(1+a1${\mathit{e}}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\beta}}}$+...) as \ensuremath{\beta}\ensuremath{\rightarrow}\ensuremath{\infty}. For q=4, the model is disordered even at zero temperature.