Probability-changing cluster algorithm for two-dimensionalXYand clock models

Abstract

We extend the newly proposed probability-changing cluster (PCC) Monte Carlo algorithm to the study of systems with the vector order parameter. Wolff's idea of the embedded cluster formalism is used for assigning clusters. The Kosterlitz-Thouless (KT) transitions for the two-dimensional (2D) XY and q-state clock models are studied by using the PCC algorithm. Combined with the finite-size scaling analysis based on the KT form of the correlation length, ξ ∝ exp(c/ T /TKT − 1), we determine the KT transition temperature and the decay exponent η as TKT = 0.8933(6) and η = 0.243(5) for the 2D XY model. We investigate two transitions of the KT type for the 2D q-state clock models with q = 6, 8, 12, and for the first time confirm the prediction of η = 4/q 2 at T1, the low-temperature critical point between the ordered and XY-like phases, systematically.

Critical properties of 2D Z(N) vector models for N>4

“…Monte Carlo simulations of the standard version with N = 6, 8, 12 were performed in Ref. [6]. Results for the critical index η agree well with the analytical predictions obtained from the Villain formulation of the model.…”

“…[7,8] and those for N = 6, 8 and 12 of Ref. [6], one can verify that β (1) c (N) approaches the 2D XY value, β (1) c = 1.1199, exponentially in N or even faster, while β (2) c (N) grows to infinity with N 2 . A more detailed analysis of the N-behavior of critical couplings will be given elsewhere [15].…”

Probability-Changing Cluster Algorithm: Study of Three-Dimensional Ising Model and Percolation Problem

“…It is also interesting to extend the PCC algorithm to the problem of the vector order parameter. We have already succeeded in applying the PCC algorithm to the classical XY model, 24) and have shown that the PCC algorithm is useful not only for the analysis of the second-order transition but also for that of the transition of the Kosterlitz-Thouless type.…”

Critical behavior of two-dimensional spin systems under the random-bond six-state clock model

“…The clock model, being a bridge between different models, is expected to have various critical behavior under different values of q. Extensive studies [8][9][10][11][12][13][14][15] on the clock model had shown that, for q 4, the phase transition is Ising-like, and for q ! 6, it is XY-like.…”