Perturbation theory for square-well fluids in d=2, 3

In this paper, we study the equation of state behaviour of square-well fluids in the dimensions d=2, 3 via the Zwanzig perturbation theory. As a particular point of emphasis, we focus on a result reported several years ago by Barker and Henderson that the perturbation theory may be used as a surprisingly accurate, predictive tool to locate the critical temperature of argon and xenon in d=3. Here we examine whether this facet of the Zwanzig theory is sensitive to the dimensionality of the configuration space of the system, by calculating the equation of state of krypton, modelled as a squarewell fluid, in d=3 and d=2. In d=3 we find that the critical temperature of krypton is predicted to within 15 per cent, while in d=2 an apparently different, high density transition is signalled by the theory.