The commensurate-incommensurate transition and fluctuations in two and three dimensions

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Abstract
The phase diagram for the two- and three-dimensional sine-Gordon system with incommensurability is investigated by means of the self-consistent harmonic approximation. For d = 2 we find three phases with in general discontinuous transitions between the two incommensurate (IC) phases A and B and the commensurate (C) phase, respectively. It is argued that the IC-phase A extends over a larger temperature regime than anticipated by Saito [20]. For d = 3 only the IC-phase A and the C-phase are found. The discontinuity of the IC-C transition is proportional to the ratio of the lattice parameter to the width of the domain walls. For sufficiently low and high temperatures the thermodynamics is given by the classical theory. Fluctuations decrease however the stability region of the C-phase