Position-space renormalization-group methods are used to solve the Blume-Capel model for the plane-triangular and fcc lattices. For ferromagnetic nearest-neighbor coupling, the results are similar to other recent results for the square and bcc lattices. However, since these lattices are close-packed, each of the antiferromagnetic results is distinctive. Corresponding results are also given for the lattice gas.
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Mahan et al. (1978) studied this question.
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