Domain-wall interactions. I. General features and phase diagrams for spatially modulated phases

A general formalism is developed for analyzing physical systems exhibiting uniaxial, spatially modulated, high-order commensurate phases which can be regarded as composed of homogeneous domains separated by ``smooth,'' parallel domain walls. Experimental evidence for a variety of such phases is mentioned; they arise also in various discrete-variable models in d>2 spatial dimensions. The free energy may be exactly decomposed into a computationally useful form as a sum of domain-wall tensions, {Σ}, plus pair, triplet, and higher-order wall-wall interaction potentials Wₙ({lᵢ}), which depend on the wall separations lᵢ, and on temperature, etc. The principal transitions between high-order modulated phases are determined by {Σ} and the nearest-neighbor pair interaction, W₂(l), alone: only simple periodic phases, having a uniform interwall separation, are stabilized by W₂(l); more complicated mixed phases, in which the wall separations alternate between two values in a regular pattern, are a consequence of further-neighbor or, in general, many-wall interactions which also determine the interfacial tensions between coexisting modulated phases. The general form of the Wₙ({lᵢ}) at low temperature is elucidated and their explicit calculation by a transfer-matrix method for models with short-range couplings is outlined. A quasitricritical point, governed by the changing form of the wall pair interaction, is analyzed in detail.