Lattice models for liquid metals. II. Exact solution of a mean-field model

A mean-field version of a simplified model for liquid metals, which consists of a lattice gas of atoms and a collection of spinless fermions that are free to hop among occupied atomic sites, is solved exactly. Phase diagrams and phase transition properties are studied for two special cases. It is found that when the fermion hopping energy is small, the presence of the fermions in the system does not change the qualitative feature of the phase diagrams as compared with the pure lattice-gas system. When the hopping energy becomes large, the system can have up to three phases and two critical points. For the case where the fermion density is proportional to the lattice-gas atomic density with the proportionality constant not equal to 1, there are two distinct critical points. For the case where the fermion density is a constant or where ther fermion density is equal to the lattice-gas atomic density the system has a tri-critical point. The system exhibits different phase transition properties under different thermodynamical conditions.