Transition-Temperature Dependences for Diluted Magnetic Systems

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Abstract
Diluted ferromagnetic and antiferromagnetic Heisenberg systems have been studied by means of three different cluster techniques. The results of two of these methods closely resemble the molecular-field-theory results. The third technique, the usual Bethe-Peierls-Weiss approximation, is shown to have a strong-spin-size-dependent critical concentration for ferromagnetic coupling in contradiction to a rigorous theorem by Rushbrooke and Morgan, while for the antiferromagnetic case no critical concentration exists at zero temperature.

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