Optimal Monte Carlo updating

Lode Pollet, Stefan M. A. Rombouts, Kris Van Houcke, and Kris Heyde
Phys. Rev. E 70, 056705 – Published 17 November 2004

Abstract

Based on Peskun’s theorem it is shown that optimal transition matrices in Markov chain Monte Carlo should have zero diagonal elements except for the diagonal element corresponding to the largest weight. We will compare the statistical efficiency of this sampler to existing algorithms, such as heat-bath updating and the Metropolis algorithm. We provide numerical results for the Potts model as an application in classical physics. As an application in quantum physics we consider the spin 32XY model and the Bose-Hubbard model which have been simulated by the directed loop algorithm in the stochastic series expansion framework.

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  • Received 10 May 2004

DOI:https://doi.org/10.1103/PhysRevE.70.056705

©2004 American Physical Society

Authors & Affiliations

Lode Pollet*, Stefan M. A. Rombouts, Kris Van Houcke, and Kris Heyde

  • Vakgroep Subatomaire en Stralingsfysica, Proeftuinstraat 86, Universiteit Gent, Belgium

  • *Electronic address: Lode.Pollet@UGent.be

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Issue

Vol. 70, Iss. 5 — November 2004

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