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A model of a monolayer of atoms adsorbed on a crystalline surface is discussed. When the initial incommensurability, , between a reciprocal lattice vector of the monolayer and one of the substrate is small, the monolayer has a one-dimensional superstructure with period depending on. For >₂ (T) the state is incommensurate; ₂ (T) decreases and vanishes at a T₂ given by the elastic moduli of the monolayer. The spectrum of small oscillations has two acoustic branches, one vanishing at the phase transition.
Pokrovsky et al. (Mon,) studied this question.