Domain-wall interactions. II. High-order phases in the axial next-nearest-neighbor Ising model

A general formalism recently introduced for the study of physical systems exhibiting uniaxial, spatially modulated commensurate phases is applied to the axial next-nearest-neighbor Ising (ANNNI) model in d>2 dimensions with arbitrary interlayer coordination numbers. Asymptotically exact low-temperature expressions for the domain-wall tension, and for the pair, triplet, and higher-order wall-wall interaction potentials characterizing the low-temperature phases, are calculated explicitly by a transfer-matrix method. The wall interaction potentials determine the phase diagram at low temperatures and reveal a new infinite sequence of mixed phases, 〈$2^k$ ${32}^{k+1\mathrm{}}$3〉 (k=1,2,. . .). Some confusing discrepancies in earlier work are resolved and certain approximations are exhibited as limiting cases of the general results. The limit of infinite coordination numbers yields the exact low-temperature mean-field hase diagram, which, contrary to some speculations, is seen to be qualitatively correct in the low-temperature limit.