Liquid state theories and critical phenomena

TLDR

The paper reviews critical behavior in liquid state theories, emphasizing universal and non‑universal properties, and investigates the microscopic definition of the order parameter in mixtures and the origin of strong crossover phenomena in binary fluids. The authors examine simple lattice and continuous models, such as the Ising model and Lennard‑Jones fluid, using integral equation methods and renormalization‑group analysis, and generalize the hierarchical reference theory to binary fluids to describe possible critical behaviors. They present a self‑contained derivation of the hierarchical reference theory, discuss its universal properties in a simple approximation, and apply it to simple models, comparing the results with other investigations.

Abstract

Abstract The description of the critical behaviour within liquid state theories is reviewed with emphasis on both the universal and the non-universal properties. Simple lattice and continuous models, such as the Ising model and the Lennard-Jones fluid, are examined by the use of several techniques, ranging from the integral equation method to the renormalization group analysis. A self-contained derivation of the hierarchical reference theory (HRT) of fluids is given together with a detailed discussion of the universal properties within a simple approximation to the exact HRT equations. Applications to simple models and comparisons with the results of other investigations are presented. HRT is then generalized to binary fluids, allowing for a complete description of the possible critical behaviours in these systems. The problems of a microscopic definition of the order parameter in mixtures and of the origin of strong crossover phenomena in binary fluids are also addressed.