Low temperature expansions around the multiphase point of an hcp Ising model with competing interactions

A low-temperature expansion is derived for the ferromagnetic phase boundary of an hcp Ising model with competing interactions, near its multiphase point, to second order in x=exp(-2D/T), where D is the ferromagnetic interplane coupling. The coefficient of x2 is a slowly converging two dimensionally infinite sum. The resulting phase boundary coincides to order x2 with the line onto which Domany mapped a two-dimensional kinetic Ising model. This lends support to the conjecture of Domany and Gubernatis that this special line coincides with the exact ferromagnetic phase boundary.