Thermodynamics of random Heisenberg models in a cluster approximation

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Abstract
The free energy of a spin-1/2 random Heisenberg ferromagnet has been calculated by a cluster approximation originally due to Strieb et al. The approximation includes contributions up to two-site spin clusters. Both the bond disorder and the site disorder cases have been considered. Using these free-energy expressions, we have obtained the expressions for the Curie temperature, specific heat, and susceptibility. We have also considered the cases of bond dilution and site dilution. Our results for these cases give a new type of behavior which earlier approximations failed to give.