Onsager reaction-field theory for magnetic models on diamond and hcp lattices

The Onsager reaction-field (ORF) theory is extended to apply to three-dimensional Bravais lattices with a basis. The ORF calculation is used to predict the critical temperature for classical Ising, $XY,$ and Heisenberg magnetic models, in particular, on diamond and hexagonal close-packed lattices. Results are compared with series extrapolations and other theoretical approaches where available. For the hcp lattice the ORF calculation is seen to be equivalent to a Green’s-function approach by Adler [Physica B&C 107B, 207 (1981)].