2003/06/05 by P. Dayal, S. Trebst, S. Wessel +4
Physics and Astronomy · #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevlett.92.097201
published as Phys. Rev. Lett. 92, 097201 (2004) · 5 pages, 6 figures
arxiv created 2003/06/05 · arxiv updated 2009/11/30
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.