Open Access

Hans Peter Neumann

• The cooperative problem for a lattice gas on a plane, square lattice and on a simple cubic lattice is solved by a system of two coupled, transcendental equations, derived by a combinatorial method, which describes a homogeneous or periodical particle density on the lattice as a function of the temperature and the chemical potential of the lattice-gas. For the particle interaction a Hard-Core potential (nearest neighbour exclusion) with a soft long-range tail is assumed. The zero-component of the Fourier-transform of this long-range interaction part can be positive or negative. The system of transcendental equations is solved by a graphic method. As a result, the complete pressure-density state diagram and the pressure-temperature phase diagram can be drawn. The lattice-gas exists in three stable phases: gas, liquid and solid. Three phase changes are possible: condensation, crystallization and sublimation. Critical points of condensation and freezing are examined. The number of possible phases and phase changes at a fixed temperature depends on the geometric structure of the particle interaction.