Optimal Monte Carlo Updating

Details Optimal Monte Carlo Updating Optimal Monte Carlo Updating

2004-05-07

arxiv.org/abs/cond-mat/0405150v2

Phys. Rev. E 70, 056705 (2004)

Physics

Condensed Matter

Other Condensed Matter

6 pages, 5 figures, replaced with published version

Scientific paper

10.1103/PhysRevE.70.056705

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 3/2 XY 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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