Regensburg 2004 – wissenschaftliches Programm

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DY: Dynamik und Statistische Physik

DY 16: Phase Transitions

DY 16.5: Vortrag

Montag, 8. März 2004, 17:45–18:00, H2

Performance Limitations of Flat Histogram Methods — •Simon Trebst — Theoretische Physik, Eidgenoessische Technische Hochschule Zuerich, CH-8093 Zuerich, Schweiz

We determine the optimal scaling of local-update flat-histogram methods with system size by using a perfect flat-histogram 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 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 Fréchet extremal value distribution that obeys exponential scaling. The shape parameter of these distributions furthermore indicate that statistical sample means become ill-defined already for moderate system sizes within these complex energy landscapes. We discuss ways to overcome these limitations by improved sampling mechanisms.

References: P.Dayal, S.Trebst, S.Wessel, D.Wurtz, M.Troyer, S.Sabhapandit, S.N.Coppersmith, cond-mat/0306106, accepted for publication in Phys. Rev. Lett.