Distribution of dimers on a plane square lattice in the Percus–Yevick approximation

The total and direct correlation matrices of the distribution of dimers on a square lattice are calculated in the Percus–Yevick approximation. The solution that correctly describes the thermodynamic behavior of a lattice gas of dimers is distinguished among several solutions of the system of equations for the elements of the direct correlation matrix. The difference between the thermodynamic functions calculated by means of this solution and the functions found by extrapolating the power-law expansions becomes appreciable only near the closely packed state of the lattice gas and in this region does not exceed $6\%$.