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Efficient Monte Carlo Simulation Methods in Statistical Physics

  • Conference paper
Monte Carlo and Quasi-Monte Carlo Methods 2000

Abstract

The basic problem in equilibrium statistical mechanics is to compute phase space average, in which Monte Carlo method plays a very important role. We begin with a review of nonlocal algorithms for Markov chain Monte Carlo simulation in statistical physics. We discuss their advantages, applications, and some challenge problems which are still awaiting for better solutions. We discuss some of the recent development in simulation where reweighting is used, such as histogram methods and multicanonical method. We then discuss the transition matrix Monte Carlo method and associated algorithms. The transition matrix Monte Carlo method offers an efficient way to compute the density of states. Thus entropy and free energy, as well as the usual thermodynamic averages, are obtained as functions of model parameter (e.g. temperature) in a single run. New sampling algorithms, such as the flat histogram algorithm and equal-hit algorithm, offer sampling techniques which generate uniform probability distribution for some chosen macroscopic variable.

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Author information

Authors and Affiliations

  1. Department of Computational Science, National University of Singapore, Singapore, 119260, Republic of Singapore

    Jian-Sheng Wang

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  1. Jian-Sheng Wang
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Editors and Affiliations

  1. Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong SAR, China

    Kai-Tai Fang  & Fred J. Hickernell  & 

  2. Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore, 117543, Republic of Singapore

    Harald Niederreiter

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© 2002 Springer-Verlag Berlin Heidelberg

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Wang, JS. (2002). Efficient Monte Carlo Simulation Methods in Statistical Physics. In: Fang, KT., Niederreiter, H., Hickernell, F.J. (eds) Monte Carlo and Quasi-Monte Carlo Methods 2000. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56046-0_9

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  • DOI: https://doi.org/10.1007/978-3-642-56046-0_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42718-6

  • Online ISBN: 978-3-642-56046-0

  • eBook Packages: Springer Book Archive

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