Morse-type Frenkel-Kontorova model

We have investigated a generalized Frenkel-Kontorova model with a Morse-type potential which can change from a convex function to a nonconvex one as the nonlinearity parameter σ is reduced. For small enough σ, there appear in the phase diagram nonconvex phases in which at least one pair of atoms is influenced by the nonconvex part of the Morse potential. There are no incommensurate states in the nonconvex phases. For σ>0.35, a devil’s staircase along the critical points of the Aubry transitions of all incommensurate states can be constructed. We studied the universality of the Hausdorff dimension of the devil’s staircase, and of some critical exponents relevant to the Aubry transitions.