Abstract
The Green function diagrammatic technique is used to examine systems with dipolar and quadrupolar pair interactions and single-ion anisotropy. To the first order in z -1, we derive the thermodynamic quantities and examine their behavior in the low and high temperature regions for various limiting cases. The zero point motion and the ground state energy are calculated. We also show in the Ising case, the quadrupolar ordered phase exists only within a finite range of single-ion anisotropy, which excludes the case with zero single-ion anisotropy for f.c.c. lattice in contradiction to the mean field prediction. Phase diagrams are discussed.
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