Theory of Random Mixtures of Ising Spins

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Abstract
Magnetic properties of the annealed quenched systems each in the bond and site models are investigated by the Kikuchi pair approximation. In the annealed system, phase diagrams and susceptibilities are obtained. Two critical temperatures in some case in the bond system and no critical concentration in the site system are obtained. The physical interpretation of them is given. In the quenched system, two different approximate conditions are considered for the complete randomness. The case of the first condition is equivalent to the cluster variation method proposed by Sato, Arrott and Kikuchi, and the results are in agreement with those obtained by Katsura and Matsubara. The second is essentially equivalent to the average coordination number method by Sato, Arrott and Kikuchi for the dilute ferromagnetism. However, the results for both cases are unreliable at low temperatures, because of the appearance of negative entropy. This is inevitable under the pair condition.

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