Wall wandering and the dimensionality dependence of the commensurate-incommensurate transition

The effect of the fluctuation-induced wandering of the domain walls (or "solitons") on the nature of the uniaxial commensurate-incommensurate phase transition at low temperature in a d-dimensional system is treated didactically using simple phenomenological arguments which are checked by lattice calculations for $d=2$. It is found that the domain wall density, or incommensurability, q̄(δ), measuring the deviation from the commensurate wave vector, vanishes with the driving potential (or temperature), δ, as (δ-δc)^β with β=(3-d)2(d-1) for $1 ~3$ the classical result q̄~1/ln(δ-δc)^-1 always applies (in disagreement with a calculation by Nattermann suggesting β=1/2 for d≥2).