Dependence of Lattice Gas Properties on Mesh Size

Abstract

The way in which the properties of a lattice gas converge to the properties of a real gas as the number of sites covered per particle is increased, till configuration space is a continuum, is investigated. Only for one-dimensional hard lines have the properties been worked out exactly for any mesh size, with the result that at any density the free volume per particle must span at least 50 lattice sites for the lattice gas pressure to approximate the real gas pressure within 1%. In the limit of close packing the lattice gas leads to an incorrect asymptotic form of the pressure for any finite mesh size. The virial coefficients for a lattice gas with a coarse spacing can be shown to differ in order of magnitude from the real gas coefficients. Inequalities between the real gas configurational integral and the lattice gas configurational sum can be established in any number of dimensions. Finally, by relating lattice and real gas results, an approximate way is found to predict properties of real gases in two and three dimensions from lattice results alone.