Vertically extended Frenkel-Kontorova model: a real space   renormalization group study
  A modification of the Frenkel-Kontorova model is presented in which particles are allowed to move in the vertical direction. This model is used to study the formation of islands for a monolayer of 1D interfaces and the corresponding roughness transition. Both analytical and numerical approaches are employed, and the numerical algorithm is based upon real space renormalization group techniques. 
Javier Rodriguez-Laguna, Silvia N. Santalla