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Title: Optimality of Wang-Landau sampling and performance limitations of flat histogram methods
Authors: Trebst, S.
Dayal, P.
Wessel, S.
Wurtz, D.
Troyer, M.
Sabhapandit, Sanjib
Issue Date: 2003
Publisher: AIP conference Proceedings
Citation: The Monte Carlo Method in the Phydcal Sciences: Celebrating the 50th Anniversary of the Metropolis Algorithm. AIP Conference Proceedings, 2003, V.690
Abstract: We determine the optimal scaling of local-update flat-histogram methods (such as multicanonical, broad histograms, tempering, or Wang-Landau sampling) with system size by using a perfect flat-histogram scheme based on the exact density of states of 2D Ising models. We find that the Wang-Landau algorithm shows the same scaling as the perfect scheme and is thus optimal. However, even for the perfect scheme the scaling with the number of spins N is slower than the minimal N2 of an unbiased random walk in energy space for both, local and N-fold way updates. While it still follows a power law N2Lz for the ferromagnetic and fully frustrated Ising model we find exponential scaling of the tunneling times in the case of the +/-J Ising spin glass. The tunneling times of the +/-J Ising spin glass are found to follow a fat-tailed Fréchet extremal value distribution.
Description: Restricted Access. An open-access version is available at (one of the alternative locations)
ISSN: 0094-243X
Alternative Location: 10.1063/1.1632165
Copyright: 2003, AIP Conference Proceedings
Appears in Collections:Research Papers (TP)

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