We investigate the phase structure of the three-state Potts model by the variational cumulant expansion approach. It is shown that there is a weak first-order phase transition in three and four dimensions. The critical coupling given by this method is in good agreement with MC data.
We investigate the phase transition of the three-state Potts model in an analytical approach—the generalized cumulant expansion with the effective mean field hypothesis. We find a first order phase transition in the three-dimensional three-state Potts model with ferromagnetic nearest neighbor coupling. For the model with antiferromagnetic next-to-nearest neighbor coupling, we find a first order transition when the relative strength of the -coupling is fixed to . The critical values given by this method are also in agreement with the recent high statistics Monte Carlo results.
Critical properties of the q-state Potts and Potts-lattice-gas models are calculated by means of the Kadanoff variational renormalization group for dimensions 1.58, 2, and 2.32, and the Migdal approximation for arbitrary dimensions. Accurate results for the critical and tricritical exponents are obtained as well as for qc, the largest value of q for which the Potts transition is continuous. It is concluded unambiguously that the three-state Potts model in three dimensions undergoes a first-order phase transition.
Abstract We report a numerical study of the weakly diluted 4-state Potts model on a triangular lattice using Monte Carlo method. We consider systems with linear dimensions L × L = N, L = 10–160. Phase transitions in the Potts model are investigated employing the fourth-order Binder cumulants method and the histogram data analysis. Second-order phase transitions which are close to weakly first-order transitions are shown to occur in the 4-state Potts model on a triangular lattice. The addition of a nonmagnetic disorder has a stabilizing role in the realization of second-order phase transitions.