Thermodynamic Functions for Fluids and Ferromagnets near the Critical Point

Modifications to the classical analysis of equilibrium thermodynamic properties near the liquid-vapor critical point are proposed in order to allow for infinite singularities in $C_v$, nonclassical behavior of the co-existence curve, etc. A requirement that all thermodynamic functions for the homogeneous fluid be analytic is retained and turns out to be necessary in order to justify Maxwell's prescription for modifying the Van der Waals equation of state. A corresponding analysis is presented for ferromagnets near the Curie point. Widom's proposed "homogeneous" equation of state is discussed with special attention to requirements of thermodynamic stability. Several examples of such homogeneous functions are constructed, including cases where the critical indices agree (very nearly, at least) with current estimates for two- and three-dimensional Ising models.