Coexistence curves for fourth-neighbor Ising models on the face-centered-cubic lattice

In this paper we investigate the influence of the range of the potential on the phase diagram for higher-neighbor Ising systems on the face-centered-cubic lattice. The density weight factors and lattice constants needed to evaluate the diagrams that contribute to the first six terms in the high-temperature expansion at arbitrary density are obtained. The resulting expression for the free energy is in the form of a series in the density and the four coupling constants ${J}_{1}$, ${J}_{2}$, ${J}_{3}$, and ${J}_{4}$ describing the potential energy as a function of interatomic distance. Differentiation of this expression with respect to density yields a series for the chemical potential. The phase diagram is obtained by straightforward analysis of this series. The results show that the coexistence curve depends on the effective number of nearest neighbors but is insensitive to the shape of the potential.