Domain-wall interactions. III. High-order phases in the three-state chiral-clock model

A general formalism recently introduced for the study of physical systems exhibiting uniaxial, spatially modulated commensurate phases is applied to the three-state chiral clock (${\mathrm{CC}}_3$) model in d>2 dimensions with arbitrary coordination numbers, $q_0$ in-layer and $q_1$ between layers. Asymptotically exact low-temperature expressions for the domain-wall tension, and for the pair and triplet wall-wall interaction potentials, are calculated explicitly by a transfer-matrix method. The wall interaction potentials determine the phase diagram at low temperatures. The results are compared with those of a similar analysis for the axial next-nearest-neighbor Ising (ANNNI) model, reported in part II: qualitative differences in the phase diagrams directly reflect the different forms of the domain-wall interactions in the two models. The limit of infinite coordination numbers yields the exact low-temperature mean-field phase diagram, which is seen to be qualitatively incorrect for describing the original, $q_1$=2 ${\mathrm{CC}}_3$ model; the phase diagrams for $q_1$≥4 exhibit a quasitricritical point on the phase boundary between the modulated and single-domain phases.