Interface phenomenology, dipolar interaction, and the dimensionality dependence of the incommensurate-commensurate transition

Previous results on fluctuation-induced domain wall wandering in continuous systems and its influence on the nature of the uniaxial incommensurate-commensurate transition are unified in a phenomenological interface theory. A relation between the exponents beta and psi describing the vanishing of the domain wall density with the driving parameter delta , and the divergence of the effective wall width for vanishing pinning potential, respectively, is established. If psi is linear in the dimensionality, d, we get for d R >or=d>or=d c , beta =(d R -d)/2(d-d c ). The critical dimensionalities d R and d c depend on the model under consideration. The changeover from the weak to the strong fluctuation regime is characterised by the different behaviour of the wall correlation length xi perpendicular to . If walls separate domains of opposite polarisation, dipolar interaction increases the stiffness of the walls and decreases d R and d c . Their values for thermal, quantum and random field fluctuations are calculated. In the dipolar case, frozen impurities lead to a lower critical dimensionality d c =2 and beta = 1 / 2 for d=3, in agreement with experiments.