A Van Der Waals Fixed Point

Abstract

In recent years, the interest of both experimentalists and theoreticians in phase transitions has been centered on the non-analytic behavior of thermodynamic and other properties in the neighborhood of a critical point or continuous phase transition [1]. In pursuing this interest it has been easy to lose sight of the fact that global features of many phase transitions are satisfactorily described by a physical picture which in the context of liquid-vapor phase transitions is called the Van der Waals theory, and in the context of magnetism, the mean-field theory. This physical picture is exact for the weak long range force model in which the forces are infinite ranged but weak in such a way that the product of the potential and the volume in which the force operates is finite [2]. Recently, in the course of an attempt to apply the scaling theory of critical phenomena and its extensions to the liquid-vapor transition in SF6 by M. Ley-Koo and the author [3], it became apparent that the Van der Waals theory may be more than a qualitative guide but may rather form the basis for a quantitative representation of the data to within a few percent of the critical density. It would appear that an adequate theory of the liquid-vapor phase transition requires a model with short range forces near the critical point and the weak long range force model far from the critical point.