Analytical method for the calculation of the phase diagram of a two-component lattice gas

We propose a new analytical method for calculating the phase diagram of a two-component lattice gas with arbitrary complex crystal lattice and any long-range order in atomic distribution. The method is elaborated in the context of a modified thermodynamic perturbation theory with the use of the inverse effective number of atoms interacting with one fixed atom as a small parameter of expansion. By a comparison with the results of the Monte Carlo simulation, the high numerical accuracy of the method is demonstrated in a wide concentration interval. The effective radius of atomic interactions is not limited within the method and the numerical accuracy of the method becomes higher with increasing radius. The developed approach may also be followed in studies of magnetics within the Ising model, of alloys, fluids and amorphous materials within the lattice gas model as well as in investigations of the low-dimension lattice systems.