Bethe approximation in the Ising model with mobile impurities

The Bethe approximation as applied to a system consisting of magnetic and nonmagnetic atoms in the thermodynamic equilibrium has been considered. In this approximation, the dependences of the magnetization and Curie temperature on the concentration of magnetic atoms for the Ising model with mobile nonmagnetic impurities have been constructed and the limiting concentrations of the appearance of spontaneous magnetization in the ground state have been obtained. It has been established that the considered approximation for a one-dimensional chain is the exact solution.