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

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

2003-06-05

arxiv.org/abs/cond-mat/0306108v1

Phys. Rev. Lett. 92, 097201 (2004)

Physics

Condensed Matter

Statistical Mechanics

5 pages, 6 figures

Scientific paper

10.1103/PhysRevLett.92.097201

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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