One-Dimensional Phase Transitions in the Spherical Lattice Gas From Inverse Power Law Potentials

The spherical model of the lattice gas of Gersch and Berlin is studied by making an integral approximation to the Fourier coefficients of the interaction potential. A phase transition is found in one dimension for potentials -gr -a with 1 \u3c α \u3c 2. A necessary condition which a potential must satisfy to allow a 1-dimensional phase transition is given. General expressions are derived for specific heat Cv and isothermal compressibility KT. Discontinuities are found in the thermodynamic properties at the transition for α less than 3/2 times the number of dimensions. Asymptotic expansions are given for Cv and KT near the critical point