Commensurate-incommensurate transitions and a floating devil's staircase

Renormalization-group equations for the uniaxial commensurate-incommensurate (C-IC) transition in two dimensions are derived. The soliton density ρ is a nonanalytic function of the misfit parameter μ even at high temperatures where only a floating phase (i.e., algebraic correlations with exponent η) is possible. The singularity at μ→0 is ρ-T_μ~μ^η-3, where T is temperature. In the (T,μ) plane the floating phase is singular therefore on all lines where its density (relative to the substrate) is rational; this is the remnant of the low-temperature devil's staircase. At low temperatures a matching procedure with the fermion approach is obtained.