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Monte Carlo algorithms based on the number of potential moves

Jian-Sheng Wang·Lik Wee Lee
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Abstract

We discuss Monte Carlo dynamics based on _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, _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.

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Jian-Sheng Wang, Lik Wee Lee. 1999-03-15. Monte Carlo algorithms based on the number of potential moves. https://doi.org/10.1016/s0010-4655(00)00016-3

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