Waste-recycling Monte Carlo with optimal estimates: application to free energy calculations in alloys

Abstract

The estimator proposed recently by Delmas and Jourdain for waste-recycling Monte Carlo achieves variance reduction optimally with respect to a control variate that is evaluated directly using the simulation data. Here, the performance of this estimator is assessed numerically for free energy calculations in generic binary alloys and compared to those of other estimators taken from the literature. A systematic investigation with varying simulation parameters of a simplified system, the anti-ferromagnetic Ising model, is first carried out in the transmutation ensemble using path-sampling. We observe numerically that (i) the variance of the Delmas-Jourdain estimator is indeed reduced compared to that of other estimators; and that (ii) the resulting reduction is close to the maximal possible one, despite the inaccuracy in the estimated control variate. More extensive path-sampling simulations involving a FeCr alloy system described by a many-body potential additionally show that (iii) gradual transmutations accommodate the atomic frustrations, thus alleviating the numerical ergodicity issue present in numerous alloy systems and eventually enabling the determination of phase coexistence conditions.

20 pages, 9 figures

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Cited by in corpus (5)

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• Estimating time-correlation functions by sampling and unbiasing dynamically activated events
• A self-contained algorithm for determination of solid-liquid equilibria in an alloy system
• Using Markov transition matrices to generate trial configurations in Markov chain Monte Carlo simulations