The MFRG method is used to study the critical behaviour of the q-state Potts antiferromagnet in three dimensions. The q dependence of the critical temperature T c as well as the exponent v are derived, and the results are compared with Monte Carlo data and predictions of mean-field theory.
We present a study of the three-state antiferromagnetic Potts model in two and three dimensions, using a cluster-flip Monte Carlo simulation algorithm. The new approach enables us to perform simulations with greatly improved efficiency. We have obtained results for the ground-state entropy and critical exponents in two and three dimensions. The low-temperature phase in three dimensions is shown to have long-range order with a finite-size dependence of the magnetization and susceptibility similar to that of the XY model.