Domain-Wall Interactions and Spatially Modulated Phases

Systems displaying long-period, uniaxial, commensurate, modulated phases are analyzed for $d>\mathrm{}2\mathrm{}$ dimensions in terms of pair, triplet, quadruplet,... interactions between domain walls in an underlying ordered phase. The axial next-nearest-neighbor Ising (ANNNI) and three-state chiral clock (C${\mathrm{C}}_3$) models with coordination numbers $q_i$ are treated as examples, revealing new lowtemperature phases. The phase diagrams in the mean-field limit, $q_i\to \infty$, agree with the small-$q_i$ results for the ANNNI but not for the C${\mathrm{C}}_3$ model, in which a quasitricritical point appears when $q_1>~4$.