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 $\frac{\pi j}{\mathrm{}(2j+1)a}$ ($j=0, 1, 2, \dots$), occurs in simple, anisotropic Ising models with nn couplings $J_0$, $J_1>0\mathrm{}$, in between spin-½ layers, and competing nnn interlayer couplings $J_2=-k{J}_1$ along one axis. The free energies, interfacial tensions, and phase boundaries are found for low $T$ in $d>\mathrm{}2\mathrm{}$ dimensions.