Performance Limitations of FlatHistogram Methods
Abstract
We determine the optimal scaling of localupdate flathistogram methods with system size by using a perfect flathistogram scheme based upon 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 nearestneighbor spin glass the distribution of tunneling times is governed by a fattailed Fréchet extremal value distribution that obeys exponential scaling. Furthermore, the shape parameters of these distributions indicate that statistical sample means become ill defined already for moderate system sizes within these complex energy landscapes.
 Publication:

Physical Review Letters
 Pub Date:
 March 2004
 DOI:
 10.1103/PhysRevLett.92.097201
 arXiv:
 arXiv:condmat/0306108
 Bibcode:
 2004PhRvL..92i7201D
 Keywords:

 75.10.Hk;
 02.70.Rr;
 64.60.Cn;
 Classical spin models;
 General statistical methods;
 Orderdisorder transformations;
 statistical mechanics of model systems;
 Condensed Matter  Statistical Mechanics
 EPrint:
 5 pages, 6 figures