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The effects of the geometry of the cubic lattices on the properties of a Heisenberg antiferromagnet with first- and second-nearest-neighbour interactions are investigated. Both the Neel temperature and the quantum defect are calculated using temperature-dependent Green function theory and the random phase approximation (RPA) for all values of the exchange constants leading to antiferromagnetic order. Special attention is given to the properties of the phase transitions which occur when the exchange constraints are varied. Graphs of the Neel temperature and the quantum defect are presented to aid comparison between theory and experiment.
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Robert H. Swendsen (1973) studied this question.
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