Surface diffusion was studied within the framework of a generalized Frenkel-Kontorova model with a non-convex transverse degree of freedom. The model assumed a lattice of atoms, with a given concentration, that interacted via Morse-type forces. The lattice was subjected to a 2-dimensional substrate potential which was periodic in one direction and non-convex (Morse) in the transverse direction. The results were used to describe a complicated exchange-mediated diffusion mechanism that had recently been observed in molecular dynamics simulations.

O.M.Braun, T.Dauxois, M.Peyrard: Physical Review B, 1996, 54[1], 313-20