Analytical study of tunneling times in flat histogram Monte Carlo

Details Analytical study of tunneling times in flat histogram Monte Carlo Analytical study of tunneling times in flat histogram Monte Carlo

2005-04-27

arxiv.org/abs/cond-mat/0504698v2

Europhys. Lett., 72 (5), pp. 802-808 (2005)

Physics

Condensed Matter

Statistical Mechanics

7 pages, 4 figures, published in Europhysics Letters (2005)

Scientific paper

10.1209/epl/i2005-10303-0

We present a model for the dynamics in energy space of multicanonical simulation methods that lends itself to a rather complete analytic characterization. The dynamics is completely determined by the density of states. In the \pm J 2D spin glass the transitions between the ground state level and the first excited one control the long time dynamics. We are able to calculate the distribution of tunneling times and relate it to the equilibration time of a starting probability distribution. In this model, and possibly in any model in which entering and exiting regions with low density of states are the slowest processes in the simulations, tunneling time can be much larger (by a factor of O(N)) than the equilibration time of the probability distribution. We find that these features also hold for the energy projection of single spin flip dynamics.

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