Regensburg 2010 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 6: Poster Session I

DY 6.7: Poster

Monday, March 22, 2010, 16:00–18:00, Poster B2

Monte Carlo simulations without detailed balance — •Heitor Fernandes, Martin Weigel, and Tanja Schilling — Institut für Physik, Johannes-Gutenberg-Universität Mainz, Staudinger Weg 7, D-55099 Mainz, Germany

Monte Carlo simulations are used to study simple systems where the underlying Markov chain satisfies the necessary condition of global balance but does not obey the more restrictive condition of detailed balance. These non-reversible Markov chains generate correct stationary distributions and have been used for a long time with the aim of decreasing autocorrelation times between consecutive measurements in sequential updates for spins systems and, e.g., for the checkerboard decomposition used in parallel architectures.

The aim of this work is to explore schemes where non-reversible dynamics is present. Our approach is based on splitting the dynamics into a set of replicas, where each of them represents a biased movement in reaction-coordinate space. This introduction of an additional bias in a given replica is compensated for by choosing an appropriate dynamics on the other replicas such as to ensure the validity of global balance.

We start by applying this method to a mean field Ising model, splitting the system into two replicas: one trying to increase magnetization and the other trying to decrease it. For this simple test system, our results show that the altered dynamics is able to reduce the dynamical critical exponent, in agreement with results from Turitsyn et al. (arXiv:0809.0916). Generalizations of this scheme to 2D-Potts models using canonical and multicanonical ensembles are discussed.