Revised Scaling Equation of State at the Liquid-Vapor Critical Point

By a simple change of variables, the scaling hypothesis of Widom is extended to apply not only to those liquid-vapor models for which it was originally designed, but also to those recently discovered models that violate the law of rectilinear diameters. "Corrections to scaling," i.e., additional terms in the equation of state beyond the homogeneous one, are shown in general not to make contributions to the singularities characteristic of these models, comparable to those coming from the change in scaling variables. Therefore, these models cannot be regarded as evidence in support of such proposed correction schemes. A more elaborate revision fo the scaling hypothesis proposed by Widom and Stillinger, is shown to be implied by the simple one proposed here.

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