  In this present paper, the recurrence equations of an Ising model with three
coupling constants on a third-order Cayley tree are obtained. Paramagnetic and
ferromagnetic phases associated with the Ising model are characterized. Types
of phases and partition functions corresponding to the model are rigorously
studied. Exact solutions of the mentioned model are compared with the numerical
results given in Ganikhodjaev et al. [J. Concr. Appl. Math., 2011, 9, No. 1,
26-34].
