Spin-glass phase in the site Ising model

For a random mixture of A and B spins in the site Ising model, with exchange energies J AA , J BB and J AB and the concentrations p A and p B , it is shown that it is possible for a spin-glass phase to exist for certain combinations of exchange energies and concentrations. The critical temperatures for paramagnetic-ferromagnetic, paramagnetic-antiferromagnetic and paramagnetic-spin-glass transitions, and the uniform, staggered, and spin-glass susceptibilities are obtained in the Bethe approximation. The Luttinger and Mattis models are also discussed.