The theory of the random Ising model formulated in terms of the distribution function of the effective field in the pair and in the cluster approximations is reviewed. An integral equation for the distribution function is derived. The integral equation has a solution for the paramagnetic state, a solution for the ferromagnetic state, a solution for the antiferromagnetic state, and solutions for the spin glass state. The phase diagram, and the ground state energy and entropy are calculated. The ground state entropy of the model is shown to be a small positive quantity contrary to the Sherrington-Kirkpatrick infinitely long-ranged model. The phase diagram derived from the cluster approximation well explains the experimental phase diagrams, in particular, of fcc spin glass and the spin glass of EupSr1-pS. The distribution function for the spin glass in the pair approximation at T = 0 with a continuous distribution is obtained analytically. They are composed of δ-functions or of δ-functions and a quadratic continuous function.
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Shigetoshi Katsura (1986) studied this question.