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 x2 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 x2, along the line y=1-x. The resulting limit of stability for the ferromagnetic phase coincides to order x2, 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.