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

Abstract

We present a detailed description of the idea and procedure for the newly proposed Monte Carlo algorithm of tuning the critical point automatically, which is called the probability-changing cluster (PCC) algorithm [Y. Tomita and Y. Okabe, Phys. Rev. Lett. {\bf 86} (2001) 572]. Using the PCC algorithm, we investigate the three-dimensional Ising model and the bond percolation problem. We employ a refined finite-size scaling analysis to make estimates of critical point and exponents. With much less efforts, we obtain the results which are consistent with the previous calculations. We argue several directions for the application of the PCC algorithm.

6 pages including 8 eps figures, to appear in J. Phys. Soc. Jpn

References in corpus (2)

• Probability-Changing Cluster Algorithm for Two-Dimensional XY and Clock Models
• Crossover and self-averaging in the two-dimensional site-diluted Ising model

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• Study of the Fully Frustrated Clock Model using the Wang-Landau Algorithm
• Broad histogram relation for the bond number and its applications
• Transfer-matrix approach to the three-dimensional bond percolation: An application of Novotny's formalism
• Novel Monte Carlo algorithms and their applications
• Exploring percolation phase transition in the three-dimensional Ising model with machine learning