The convergence of perturbation expansions in classical statistical mechanics

Abstract

The most successful theory of liquids is perturbation theory in which the attractive energy is treated as a perturbation on the hard-sphere potential and the canonical partition function expanded in powers of the perturbations. The convergence of perturbation theory in the constant pressure, canonical, and grand canonical ensembles is investigated for a one-dimensional square-well fluid, where the calculations are not too lengthy and where a comparison with exact results can be made. At high temperatures, the convergence is excellent in all three ensembles but, at lower temperatures, the convergence is excellent in the canonical ensemble but only fair in the constant pressure and grand canonical ensembles.