Liquid state theories and critical phenomena

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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.