Monte Carlo algorithms based on the number of potential moves
arXiv:cond-mat/9903224 · doi:10.1016/S0010-4655(00)00016-3
Abstract
We discuss Monte Carlo dynamics based on <N(sigma, Delta E)>_E, the (microcanonical) average number of potential moves which increase the energy by Delta E in a single spin flip. The microcanonical average can be sampled using Monte Carlo dynamics of a single spin flip with a transition rate min(1, <N(sigma', E-E')>_E' / <N(sigma, E'-E) >_E) from energy E to E'. A cumulative average (over Monte Carlo steps) can be used as a first approximation to the exact microcanonical average in the flip rate. The associated histogram is a constant independent of the energy. The canonical distribution of energy can be obtained from the transition matrix Monte Carlo dynamics. This second dynamics has fast relaxation time - at the critical temperature the relaxation time is proportional to specific heat. The dynamics are useful in connection with reweighting methods for computing thermodynamic quantities.
8 pages, 4 figures, invited talk on CCP99 conference, 20-27 May 99, Atlanta, GA
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