Dresden 2003 – scientific programme
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DY: Dynamik und Statistische Physik
DY 46: Poster
DY 46.95: Poster
Thursday, March 27, 2003, 15:30–18:00, P1
Parallel Tempering at Second-Order Phase Transitions — •Andreas Nußbaumer, Elmar Bittner, and Wolfhard Janke — Institut für Theoretische Physik, Universität Leipzig, Augustusplatz 10/11, 04109 Leipzig, Germany
The parallel tempering algorithm has proved to be very powerful in accelerating Monte Carlo simulations of disordered systems with rugged free energy landscapes. The most prominent examples are spin glasses and structural glasses. One of the merits of this algorithm is its simplicity, permitting applications also to models for which cluster, multigrid or other non-local update algorithms have not yet been discovered. Having such situations in mind, we investigated whether parallel tempering can also be a useful tool at a standard second-order phase transition. As a very simple test case we considered the 2D Ising model (where, of course, cluster algorithms would be more efficient) and studied the dependence of the integrated autocorrelation time τint,M of the magnetization on the acceptance rate between replicas, on the linear size of the system, and on the number of replicas used. Using a novel FFT implementation for the estimation of the autocorrelation time, it was found that τint, M does depend only weakly on the number of replicas but strongly on the temperature distance between the replicas. In all cases τint,M was significantly reduced by parallel tempering in comparison to the standard Metropolis algorithm. This shows that parallel tempering may be a useful alternative for models for which sophisticated non-local algorithms are not available.