3-STATE POTTS ANTIFERROMAGNET ON THE TRIANGULAR LATTICE

The three-state Ports antiferromagnetic model on the triangular lattice (3PAFT) has a weak first-order transition in the pure case. The first-order nature follows from analytic arguments and while it has been observed in some simulations, the precision of (and internal disagreement between) these observations has left much to be desired. The 3PAFT is the only two-dimensional nearest-neighbour Ports model with an ordered phase that does not have an infinite degeneracy, that remains without an exact value for its critical point. This model is expected to exhibit interesting glassy behaviour and a possible crossover to a second-order transition upon dilution. A careful characterization of the nature of the pure transition is needed in order to explore the physics of the dilute model. We find clear indication of a first-order transition at T-t = 0.627 31 +/- 0.000 06, using a cluster method that can be extended to the dilute case and histogram reweighting analysis. Our estimate is two orders of magnitude more precise than previous simulations and falls within the error bounds of a reanalysis of existing series expansion (T-t = 0.628 +/- 0.004) reported on herein.