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29 March 2024
 
  » arxiv » cond-mat/0202161

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Probability-Changing Cluster Algorithm for Two-Dimensional XY and Clock Models
Yusuke Tomita ; Yutaka Okabe ;
Date 9 Feb 2002
Journal Phys. Rev. B65, 184405 (2002)
Subject Statistical Mechanics | cond-mat.stat-mech
AbstractWe 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, $xi propto exp(c/sqrt{T/T_{ m KT}-1})$, we determine the KT transition temperature and the decay exponent $eta$ as $T_{ m KT}=0.8933(6)$ and $eta=0.243(5)$ 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 {it for the first time} confirm the prediction of $eta = 4/q^2$ at $T_1$, the low-temperature critical point between the ordered and XY-like phases, systematically.
Source arXiv, cond-mat/0202161
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