Antiferromagnetic potts models on the square lattice: A high-precision Monte Carlo study.
J STAT PHYS
461 - 530.
study the antiferromagnetic q-state Potts model on the square lattice for q = 3 and q = 4, using the Wang-Swendsen-Kotecky (WSK) Monte Carlo algorithm and a powerful finite-size-scaling extrapolation method. For q=3 we obtain good control up to correlation length xi similar to 5000; the data are consistent with xi(B)=Ae(2 beta)beta(P)(1 + a(1)e(-beta) + ...) as beta--> infinity, with p approximate to 1. The staggered susceptibility behaves as chi(stagg) similar to xi(5/3). For q = 4 the model is disordered (xi less than or similar to 2) even at zero temperature. In appendices we prove a correlation inequality for Potts antiferromagnets on a bipartite lattice, and we prove ergodicity of the WSK algorithm at zero temperature for Potts antiferromagnets on a bipartite lattice.
|Title:||Antiferromagnetic potts models on the square lattice: A high-precision Monte Carlo study|
|Keywords:||Potts model, antiferromagnet, square lattice, phase transition, zero-temperature critical point, Monte Carlo, cluster algorithm, Swendsen-Wang algorithm, Wang-Swendsen-Kotecky algorithm, finite-size scaling, NONLINEAR SIGMA-MODELS, LOGARITHMIC CORRECTIONS, MULTICRITICAL POINT, PHASE-TRANSITIONS, CRITICAL-BEHAVIOR, 3 DIMENSIONS, SPIN MODELS, MASS GAP, XY-MODEL, SIMULATIONS|
|UCL classification:||UCL > School of BEAMS > Faculty of Maths and Physical Sciences
UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Mathematics
Archive Staff Only