A FORMULATION OF STATISTICAL-MECHANICS OF ORDERED SYSTEMS

Expressions are derived for the thermodynamic functions (Gibbs free en ergy, Helmholtz free energy, etc.) of an ordered system in terms of th e single-particle distribution function, rho(x), and correlation funct ions. The thermodynamic functions are treated as functionals of the si ngle-particle distribution function. By minimizing the Helmholtz free energy with respect to rho(x) under constraints of constant T, V and N , an integral equation is obtained from which rho(x) can be determined . The correlation function of the ordered state in the region near the coexistence surface between ordered and disordered state is expanded about the correlation function of the disordered state, and the series is truncated. Methods for calculating the thermodynamic functions and the single-particle distribution function are presented, and our resu lt is discussed in relation to other treatments of phase coexistence i n the literature.