Computer Simulations of Phase Transitions in Potts Models

Methods are developed to identify and characterize first-order and Kosterlitz-Thouless transitions through computer simulations. Finite-size effects at temperature-driven first -order transitions are analyzed by introducing a double -Gaussian approximation for the probability distribution of the internal energy and predictions are made for various moments of the distribution. It is found that all finite -size effects vary as the volume, L('d). The predictions are tested by simulating the 10-state Potts model in two dimensions which has a known first-order transition in zero-field. Extensive Monte Carlo simulations were performed on the Cyber 205 with L = 18 to 50 and using between 1 x 10('6) and 40 x 10('6) MCS per data point. The results are in good agreement with the Gaussian formalism enabling accurate estimates of various thermodynamic quantities of the model. The analysis is applied to an Ising model with competing interactions on a triangular lattice and the first-order transition in this model is confirmed. The Kosterlitz-Thouless transitions in the 6-state vector Potts model are studied through Monte Carlo simulations on the Cyber 750 using lattices of size 4 x 4 to 72 x 72 and up to 200,000 MCS. Two independent methods--finite -size scaling and a cumulant method--were used to analyze the data. Both methods identify the two Kosterlitz-Thouless transitions separating a low-temperature ordered phase, a high-temperature disordered phase and an intermediate with xy-like phase. The phase transitions occur at kT(,1)/J = 0.68 (+OR-) 0.02 and kT(,2)/J = 0.92 (+OR-) 0.01. The susceptibility is infinite in the intermediate phase and the exponent (eta) varies between 0.100 at T(,1) and 0.275 at T(,2). The results are in good agreement with theoretical predictions and are shown to be more accurate than previous simulational treatments.