Phase Transitions of Antiferromagnetic Potts Models

Abstract

Phase transitions of antiferromagnetic Potts models are investigated by cactus approximations and Monte Carlo simulations. These models show phase transitions associated with highly degenerate ground states. By the simulations for systems on a simple cubic lattice, a Kosterlitz-Thouless phase has been found below kT/ IJI::::e 1.25 for the three-state Potts model, while a longrange ordering consisting of two sublattices has appeared below k T/ If I : : : : e 0. 7 for the four-state Potts model. by guest on March 23, 2015 http://ptps.oxfordjournals.org/ Downloaded from

Two Types of Ordering in the Three-State Antiferromagnetic Potts Model on 3D Lattices: Monte Carlo Evidence

“…1a around the y axis) with a radius increasing with decreasing temperature. Apparently, the relevant order parameter in the critical region close to T c would be z r , which actually was used for the susceptibility calculations in previous MC calculations [4,5,11]. This result is consistent with the reported XY universality class: The free energy of the XY model is rotationally symmetric in ͗s x ͘, ͗s y ͘ space at any temperature.…”

“…Because of incomplete ordering [2] at T 0 these points never actually reach the edges. What Ono [5] found during a relatively short MC run was a very broad distribution of the instantaneous order parameter on this phase space instead of gathering around a single point, which indicates wide (or shallow) free-energy minima even well below T c . More accurate Monte Carlo simulations by Wang et al [4] based on a cluster-flip algorithm have shown that while at low temperature there clearly exist six freeenergy minima, where the order parameter points gather, corresponding to the BSS phase, at higher temperatures the distribution is more rotationally symmetric with some sixfold anisotropy, and very close to T c the distribution is almost circular (see Fig.…”

“…A secondorder phase transition at T c ͞J 1.28 6 0.04 was found to belong to the XY universality class. Later, the universality class was confirmed and the T c was refined to [5] has shown unusually large fluctuations of the probabilities for the Potts states. These fluctuations were attributed to insufficiently long MC runs, and it was suggested that equal probabilities for all states might be achieved for runs sufficiently long.…”

Ordered phase and scaling inZnmodels and the three-state antiferromagnetic Potts model in three dimensions

“…On the other hand, according to numerical calculations, there appears to be an intermediate phase below T c and above the low-temperature phase. While there have been various proposals [5][6][7] for the intermediate region, most reliable numerical results at present indicates that the intermediate region appears to be rotationally symmetric phase which is similar to the ordered phase of the 3D XY model [10][11][12] . However, the "transition" between the intermediate region and the low-temperature phase is not well understood.…”

Mean-field analysis of antiferromagnetic three-state Potts model with next-nearest-neighbor interaction

“…Since the numerical method (20) becomes less precise near the critical line, we expand the mean-field free energy F 0 in powers of the order-parameter to investigate the critical behavior.…”