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Performance Limitations of Flat Histogram Methods and Optimality of Wang-Landau Sampling

P. Dayal·S. Trebst·S. Wessel·D. Wuertz·M. Troyer·S. Sabhapandit·S. N. Coppersmith
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Abstract

We determine the optimal scaling of local-update flat-histogram methods with system size by using a perfect flat-histogram scheme based on the exact density of states of 2D Ising models.The typical tunneling time needed to sample the entire bandwidth does not scale with the number of spins N as the minimal N^2 of an unbiased random walk in energy space. While the scaling is power law for the ferromagnetic and fully frustrated Ising model, for the +/- J nearest-neighbor spin glass the distribution of tunneling times is governed by a fat-tailed Frechet extremal value distribution that obeys exponential scaling. We find that the Wang-Landau algorithm shows the same scaling as the perfect scheme and is thus optimal.

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P. Dayal, S. Trebst, S. Wessel, D. Wuertz, M. Troyer, S. Sabhapandit, S. N. Coppersmith. 2003-06-05. Performance Limitations of Flat Histogram Methods and Optimality of Wang-Landau Sampling. https://doi.org/10.1103/physrevlett.92.097201

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