Ising model on a face-centered cubic lattice at low temperatures

The phase diagram of the model is constructed in a region of infinite degeneracy of the ground state that does not contain superdegenerate points. We consider the antiferromagnetic Ising model on a face-centered cubic lattice. This model is the simplest among an entire family of models used to describe binary alloys of the type CuAu. The more complicated models contain an interaction of not only the nearest neighbors and not only two-body interactions; however, the simplest variant still possesses the characteristic properties of the complete class of models. The main aim of the present paper is to give a rigorous proof of the fact that at sufficiently low temperatures there exist limiting Gibbs distributions corresponding to these most stable ground states. In the special case h = 0, this result was also obtained by Bricmont and Slavny