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
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 N2 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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