The solid-fluid phase transition: contribution of small watermelons

Abstract

An important subset of diagrams, the small watermelons and their elementary derivatives, are found to exhibit a finite clustering property; the subset is summed approximately and provides a long-range tail to the Percus core of the direct correlation. Below a certain density, governed by the range of the small watermelons, fluid-like solutions are obtained, whilst above this density the structure is long-range oscillatory. The rigid sphere isotherm shows distinct fluid and solid branches in essential agreement with the machine simulations. The finite clustering of particles implies a dramatic development of the statistical attraction operating in the fluid, and serves to shift the system from the fluid to the solid branch of the isotherm.