Towards a unification of HRT and SCOZA. Analysis of exactly solvable mean-spherical and generalized mean-spherical models

TL;DR

This paper explores the potential unification of two liquid state theories, HRT and SCOZA, by analyzing exactly solvable mean-spherical models, demonstrating that a combined approach can recover correct solutions and clarifies their interrelation.

Contribution

It extends the mean spherical model to a generalized form and shows that both HRT and SCOZA, alone or combined, can accurately solve it, revealing their underlying connection.

Findings

Unification of HRT and SCOZA is feasible in exactly solvable models.

Both theories can independently recover correct solutions with proper boundary conditions.

The relation between HRT-SCOZA equations and individual theories is clarified.

Abstract

The hierarchical reference theory (HRT) and the self-consistent Ornstein-Zernike approximation (SCOZA) are two liquid state theories that both furnish a largely satisfactory description of the critical region as well as the phase coexistence and equation of state in general. Furthermore, there are a number of similarities that suggest the possibility of a unification of both theories. Earlier in this respect we have studied consistency between the internal energy and free energy routes. As a next step toward this goal we here consider consistency with the compressibility route too, but we restrict explicit evaluations to a model whose exact solution is known showing that a unification works in that case. The model in question is the mean spherical model (MSM) which we here extend to a generalized MSM (GMSM). For this case, we show that the correct solutions can be recovered from suitable boundary conditions through either of SCOZA or HRT alone as well as by the combined theory. Furthermore, the relation between the HRT-SCOZA equations and those of SCOZA and HRT becomes transparent.