Multiphase behavior of large interacting molecules on a flat square lattice in the Percus–Yevick approximation

In the Percus–Yevick approximation, the total and direct correlation matrices of the molecules of a lattice gas are found in the case of infinite repulsion of first neighbors and finite interaction $\varepsilon$ ($\varepsilon<0$) of second neighbors on a square lattice. Calculations are made of the thermodynamic functions, whose behavior reveals the occurrence in the system of phase transitions, which are of the continuous (of the type of ordering) and first kind. The critical temperature $x_{\mathrm c}=\exp(-\beta_{\mathrm B}\varepsilon)=2{.}933$ ($\beta_{\mathrm B}=1/k_{\mathrm B}T$ is the reciprocal absolute temperature) and the critical density $\rho_{\mathrm c}=0{.}158$ are determined. The phase diagram of the system is constructed.