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DY: Fachverband Dynamik und Statistische Physik
DY 56: Poster - Statistical Physics
DY 56.9: Poster
Donnerstag, 19. März 2015, 16:00–18:00, Poster A
Infinitesimal Monte Carlo Algorithms — •Manon Michel1, Sebastian C. Kapfer2, and Werner Krauth1 — 1Laboratoire de Physique Statistique, 24 rue Lhomond 75005 Paris France — 2Institut für Theoretische Physik 1 Staudtstr. 7 91058 Erlangen Germany
Monte Carlo methods, most notably the Metropolis algorithm, are a powerful tool in statistical physics. But local random walks induce a high rate of rejections, making any simulations around a phase transition point too expensive. To address this problem, we reformulate the Metropolis algorithm at the most fundamental level, upgrading the diffusive dynamics to a convective one. We therefore construct a new framework for Monte Carlo algorithms, based on a new factorization of the Metropolis acceptance probability. It leads to a class of rejection-free Markov chain Monte Carlo algorithms for sampling general multidimensional probability distributions, without introducing discretizations in time or in space [1]. These algorithm break detailed balance yet satisfy global balance. They generalize the recent and successful hard-sphere event-chain Monte Carlo method and were recently used in bidimensional melting with soft interactions. Finally, this new framework allows direct access to quantities as pressure and stress in multiparticle systems. Generally, it leads also to new insights on elastic constants derivation from first principles, yielding a precise determination of existence of hexatic phase[2].
[1] M. Michel, S. C. Kapfer, W. Krauth, Journal of Chemical Physics 140 54116 (2014)
[2] M. Michel, S. K. Kapfer, W. Krauth, manuscript in preparation