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DY: Fachverband Dynamik und Statistische Physik

DY 25: Statistical Physics II (General)

DY 25.4: Vortrag

Dienstag, 13. März 2018, 10:45–11:00, BH-N 243

Derivation of an optimal time-dependent bias for Wang-Landau simulations — •Andreas Heuer and Myra Biedermann — Inst. f. Phys. Chemie, WWU Münster, Germany

Among the large variety of free-energy methods, the Wang-Landau approach plays an important role due to its broad applicability, e.g., in the fields of statistical physics. Empirically, it has been observed for simulations of, e.g., the Ising model, that the added bias f(t) should be chosen as M/t for long times, where M denotes the number of bins [1].

In this contribution we analyse a simple but non-trivial model system, suggested in [2], for which the impact of a time-dependent bias can be treated analytically. Key results are: (1) a minimal error requires the choice f(t) = M/t. (2) There exists a short-time regime where the optimum bias decreases exponentially with time. (3) Surprisingly, the estimation of individual free energies is systematically biased, with the bias scaling as log(t) / t.

These results are quantitatively reproduced in simulations of the Ising model and may serve as a justification for a frequently employed application scheme for Wang-Landau simulations, the 1/t algorithm [1].

[1] R.E. Belardinelli and V.D. Pereyra, Phys. Rev. E 75, 046701 (2007). [2] R.E. Belardinelli, V.D. Pereyra, R. Dickman, B. J. Lourenco, J. Stat. Mech., P07007 (2014).