Abstract
The isotropic quadrupolar coupling Hamiltonian is studied by means of double-time Green's functions. The equations-of-motion hierarchy is decoupled by using the concepts of cumulant averages and self-consistently identifying the statistically independent operators of the system. Our results satisfy all relevant spin-1 identities. We obtain the transition temperature and the ground-state order parameter for the sc, fcc, and bcc lattices. Our result for the ground-state order parameter is larger than that obtained by current decoupling schemes.
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