Microscopic approach to critical phenomena in binary fluids

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Abstract
A first-principles theory for the description of critical phenomena in mixtures is presented. This is a natural extension of the hierarchical reference theory of fluids, which has proven useful and accurate in the treatment of the critical region of one-component fluids. The case of a binary mixture is studied in detail. Near the critical point, the theory develops a renormalization-group structure that allows the identification of several possible critical behaviors corresponding to different fixed points. For a generic binary mixture, the most stable fixed point gives rise to the same critical exponents as are predicted by the well-known phenomenological approach, providing a microscopic mechanism for such behavior. The competition between two fixed points is identified as the mechanism leading to the strong corrections to scaling seen experimentally. Explicit expressions for the most interesting universal quantities are evaluated to O(4-d). This theory is then applied to a few simple models of mixtures in three dimensions. As a first step, the mean-field phase diagram is reproduced and the stability of this solution is determined. The physical nature of the relevant order parameter and the one-loop correction to mean-field results are also calculated within our approach.

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