Statistical-thermodynamic description within the ring approximation. II. Ising model

The results obtained previously [R. V. Chepulskii, Phys. Rev. B 69, 134431 (2004)] within the ring approximation in the case of the lattice gas model are generalized to the case of the Ising model with a complex crystal lattice and arbitrary magnetic order. The nonpair spin interactions of any order and effective radii of action are taken into account. The verification of the numerical accuracy of the ring approximation in the cases that are typical at consideration of the Ising model is performed.