Effective discommensurations in the incommensurate ground states of the extended Frenkel-Kontorowa models (Q752950)

A multidimensional Frenkel-Kontorowa (FK) model is considered. Provided that the attached phonon spectrum has a nonzero gap, the authors prove that the hull function of an incommensurate ground state is purely discrete. The starting point is the well-known fact that for the 1- dimensional FK model the ground states are of two kinds: commensurate ones (periodic cycles) and incommensurate ones (KAM 1-tori). It follows readily from the result in the paper, that the Fourier coefficients of the incommensurate modulation are given by an analytic hull function.