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Phys. Rev. E 74, 026707 (2006) [11 pages]

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

Hiroshi Watanabe,1,2 Satoshi Yukawa,2 M. A. Novotny,3 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

Received 30 March 2006; revised 11 July 2006; published 30 August 2006

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(constbeta) in the Ising, sqrt( beta ) in the classical XY, and beta in the classical Heisenberg spin systems with inverse temperature beta, regardless of the dimension. The efficiency in hard particle systems is also obtained, and found to be proportional to (rhocprho)d with the closest packing density rhocp, density rho, 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.

©2006 The American Physical Society

URL: http://link.aps.org/doi/10.1103/PhysRevE.74.026707
DOI: 10.1103/PhysRevE.74.026707
PACS: 02.70.Tt; 75.10.Hk; 02.50.Ga
  • 02.70.Tt
    Justifications or modifications of Monte Carlo methods
  • 75.10.Hk
    Classical spin models (magnetism)
  • 02.50.Ga
    Markov processes
  • YEAR: 2006
KEYWORDS: Monte Carlo methods, Ising model, X-Y model, Heisenberg model, spin systems, molecular dynamics method

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