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Systems displaying long-period, uniaxial, commensurate, modulated phases are analyzed for $d>2$ 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 (CC₃) models with coordination numbers qᵢ are treated as examples, revealing new lowtemperature phases. The phase diagrams in the mean-field limit, qᵢ→∞, agree with the small-qᵢ results for the ANNNI but not for the CC₃ model, in which a quasitricritical point appears when q₁>~4.
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Szpilka et al. (1986) studied this question.
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