Static correlations of higher order and diffusion in an interacting lattice gas

Abstract

For a lattice gas with extended hard core interaction on a square lattice the static correlation functions of higher order, which determine the average jump rate in the diffusion process, are calculated both by the Monte Carlo method and by analytic approximations. It is found that the superposition approximation is very inaccurate for the correlation functions of third and fourth order, but gives better results for the average jump rate. Up to concentrations ofc = 0.3 better consistency with the Monte Carlo data for both quantities is obtained by treating the site occupation numbers as Gaussian random variables and accordingly expressing the correlation functions of higher order by products of averages of two particle correlations. For concentrationsc > 0.3, however, a Bethe-Peierls cluster approximation is superior to the superposition approximation.