Universal incommensurate structures

Certain phase transitions in quasiperiodic systems are characterized byuniversal structures. In these cases the functional form of the order parameter corresponding to the modulated phase,P(r), is determined by the symmetry properties of the system and is independent of the details of the associated Landau-Ginzburg model. Here we consider a simple one-dimensionalXY-like model corresponding to this type of phase transition. The universal modulated structure of this model is calculated numerically at various points along the critical line.