Infinitely Many Commensurate Phases in a Simple Ising Model

On the basis of systematic low-temperature expansions "to all orders", it is shown that an infinite sequence of spatially modulated commensurate phases, with wave vectors $\frac{\ensuremath{\pi}j}{(2j+1)a}$ ($j=0, 1, 2, \dots{}$), occurs in simple, anisotropic Ising models with nn couplings ${J}_{0}$, ${J}_{1}g0$, in between spin-\textonehalf{} layers, and competing nnn interlayer couplings ${J}_{2}=\ensuremath{-}k{J}_{1}$ along one axis. The free energies, interfacial tensions, and phase boundaries are found for low $T$ in $dg2$ dimensions.