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Low-temperature expansions for an Ising model on a hexagonal-close-packed lattice with competing interactions.

The limit of stability for the ferromagnetic phase of an hcp Ising model with in-plane antiferromagnetic interactions, J, and out-of-plane ferromagnetic interactions, D, is calculated with use of a low-temperature expansion. To the lowest order in x = exp(-2D/T) the limit of stability is given by y = 1-x, where y = exp(-4(1/2+J/D)/T). The calculation to order x/sup 2/ requires the summation of excitations which contribute to the free-energy terms proportional to arbitrary powers of x and y, but when summed, contribute to order x/sup 2/, along the line y = 1-x. The resulting limit of stability for the ferromagnetic phase coincides to order x/sup 2/, with the special line onto which Domany mapped a dynamical ferromagnetic Ising model on the honeycomb lattice. This strongly suggests that part of this special line exactly coincides with the ferromagnetic phase boundary.