Correlations near phase transition in a simple fluid

Abstract

Correlations in a system with a weak, long-ranged attractive potential are studied. Using a natural small parameter, the asymptotic orders of all correlations are established. Explicit leading order solutions are obtained for all correlations when the system is away from phase change As it approaches transition, It is shown that the many-body correlations, even though still small, develop very long range and that they are shown extremely slowly varying functions over space. As a results all the correlations contribut equally significantly to the computation of the pair correlation. In an asymptotic ragion near transition, a hierarchy is derived in which each corelation is expressed in terms of its immediate predecessor, its immediate successor and the pair correlation. The pair potential does not appear in these equations. Instead the correlations are expressed in terms of a Yukawa potential whose strength and range are related to the density and other parameters but not to the detailed form of the potential. In the leading approximation, the pair correlation is proportional to this Yukawa function.