Ground State, Spectrum, and Phase Diagram of Two-Dimensional Incommensurate Crystals

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.