A smooth cut-off formulation of the hierarchical reference theory of fluids

Abstract

Following the same strategy adopted in the hierarchical reference theory of fluids the author has derived a new hierarchy of differential equations for the free energy and the direct correlation functions of a classical fluid. In the critical region the equations resemble the renormalisation group in a smooth cut-off formulation and in fact the theory gives the usual epsilon =4-d expansion for the critical exponents. In this theory the universality of the critical behaviour is not manifest and it is generally lost in an approximate solution of the hierarchy. They have studied a very simple approximation in d=3 giving a non-classical value of the compressibility critical exponent and they have checked that the violation of universality is small.