Transition-Temperature Dependences for Diluted Magnetic Systems

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.