Computer Simulations of Phase Transitions in Potts Models
Abstract
Methods are developed to identify and characterize firstorder and KosterlitzThouless transitions through computer simulations. Finitesize effects at temperaturedriven 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 10state Potts model in two dimensions which has a known firstorder transition in zerofield. 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 firstorder transition in this model is confirmed. The KosterlitzThouless transitions in the 6state 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 methodsfinite size scaling and a cumulant methodwere used to analyze the data. Both methods identify the two KosterlitzThouless transitions separating a lowtemperature ordered phase, a hightemperature disordered phase and an intermediate with xylike 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.
 Publication:

Ph.D. Thesis
 Pub Date:
 1986
 Bibcode:
 1986PhDT........79C
 Keywords:

 KOSTERLITZTHOULESS TRANSITIONS;
 CLOCKMODELS;
 FINITESIZE EFFECTS;
 Physics: Condensed Matter