Complete analysis of phase behavior of an adsorption model of a binary gas mixture on a square lattice was carried out for all possible sets of lateral interactions between nearest adsorbed molecules of the same type and no interaction between adsorbed molecules of different types. The model was completely investigated in the ground state, and it was shown that the phase behavior of the system is conserved at finite temperatures by means of a transfer matrix method.

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A model of homonuclear dimer adsorption in terms of two possible molecule orientations with respect to the surface on a square lattice has been constructed and studied. The dimers can occupy one or two sites on the lattice. The thermodynamics of this system has been studied by transfer-matrix and Monte Carlo methods. The phase diagram has been constructed. It was shown that in the vicinity of the tricritical point the coverage as a function of chemical potential possesses a minimum. This phenomenon seems to be the common one for molecules with several ways of adsorption.

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