Eur. Phys. J. B 8, 287-291 (1999)
https://doi.org/10.1007/s100510050692

Is the broad histogram random walk dynamics correct?

Department of Computational Science, National University of Singapore, Singapore 119260, Republic of Singapore

Received: 2 October 1998
Revised: 13 October 1998
Published online: 15 March 1999

Abstract

We show explicitly that the broad histogram single-spin-flip random walk dynamics does not give correct microcanonical average even in one dimension. The dynamics violates the detailed balance condition by an amount proportional to the inverse system size. As a result, in distribution different configurations with the same energy can have different probabilities. We propose a modified dynamics which ensures detailed balance and the histogram obtained from this dynamics is exactly flat. The broad histogram equation relating the average number of potential moves to density of states is generally valid.