Efficiency of rejection-free dynamic Monte Carlo methods for homogeneous spin models, hard disk systems, and hard sphere systems

Hiroshi Watanabe, Satoshi Yukawa, M. A. Novotny, and Nobuyasu Ito
Phys. Rev. E 74, 026707 – Published 30 August 2006

Abstract

We construct asymptotic arguments for the relative efficiency of rejection-free Monte Carlo (MC) methods compared to the standard MC method. We find that the efficiency is proportional to exp(constβ) in the Ising, β in the classical XY, and β in the classical Heisenberg spin systems with inverse temperature β, regardless of the dimension. The efficiency in hard particle systems is also obtained, and found to be proportional to (ρcpρ)d with the closest packing density ρcp, density ρ, and dimension d of the systems. We construct and implement a rejection-free Monte Carlo method for the hard-disk system. The RFMC has a greater computational efficiency at high densities, and the density dependence of the efficiency is as predicted by our arguments.

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  • Received 30 March 2006

DOI:https://doi.org/10.1103/PhysRevE.74.026707

©2006 American Physical Society

Authors & Affiliations

Hiroshi Watanabe1,2,*, Satoshi Yukawa2,†, M. A. Novotny3, and Nobuyasu Ito2

  • 1Department of Complex Systems Science, Graduate School of Information Science, Nagoya University, Furouchou, Chikusa-ku, Nagoya 464-8601, Japan
  • 2Department of Applied Physics, School of Engineering, The University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
  • 3Department of Physics and Astronomy, and HPC2 Center for Computational Sciences, Mississippi State University, Mississippi State, Mississippi 39762-5167, USA

  • *Email address: hwatanabe@is.nagoya-u.ac.jp
  • Present address: Department of Earth and Space Science, Graduate School of Science, Osaka University, Japan.

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Issue

Vol. 74, Iss. 2 — August 2006

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