Equilibrium Times for the Multicanonical Method

Details Equilibrium Times for the Multicanonical Method Equilibrium Times for the Multicanonical Method

2004-02-06

arxiv.org/abs/cond-mat/0402191v1

Physics

Condensed Matter

Statistical Mechanics

7 pages, 5 eps figures, to be published in Int. J. Mod. Phys. C

Scientific paper

10.1142/S0129183104005851

This work measures the time to equilibrium for the multicanonical method on the 2D-Ising system by using a new criterion, proposed here, to find the time to equilibrium, teq, of any sampling procedure based on a Markov process. Our new procedure gives the same results that the usual one, based on the magnetization, for the canonical Metropolis sampling on a 2D-Ising model at several temperatures. For the multicanonical method we found a power-law relationship with the system size, L, of teq=0.27(15) L^2.80(13), and with the number of energy levels to explore, kE, of teq=0.7(13) kE^1.40(11), in perfect agreement with the result just above. In addition, some kind of critical slowing down was observed around the critical energy. Our new procedure is completely general, and can be applied to any sampling method based on a Markov process.

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