Abstract
For a Heisenberg paramagnet having both uniaxial anisotropic exchange and single-ion uniaxial anisotropy, two types of dilution are considered: model (a) in which the existence of transverse and longitudinal bonds depends only on a single random variable, and model (b) in which these bonds can fluctuate independently. For both models analytic expressions for the moments up to the fourth are presented that are valid for arbitrary spin and arbitrary range of the magnetic integration. Both the longitudinal and transverse moments are considered. The results are specialised to a number of simple lattices (linear, square, simple cubic, body-centered cubic and face-centred cubic) having nearest-neighbour and second-nearest-neighbour interactions only. Finally, the sixth frequency moment in the case of the isotropic magnet is studied using model (a).
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