Critical behavior of commensurate-incommensurate phase transitions in two dimensions

It is shown that there are no critical divergences on the commensurate side of the commensurate-incommensurate transition in the two-dimensional sine-Gordon system, whereas on the incommensurate side there are divergences of the specific heat and of the correlation length. The critical exponents are determined. The results are explained in terms of fluctuating domain walls between commensurate regions. This allows a generalization of some of the results to more complex systems.