Intricacies of nonlinearity and disorder in the Random Sine-Gordon model

Angel Sanchez

Department of Matematicas, University Carlos III de Madrid, Leganes, Madrid, Spain

Abstract: We present a comparative numerical study of the ordered and the random two-dimensional sine-Gordon models on a lattice. We analytically compute the main features of the expected high temperature phase of both models described by the Edwards-Wilkinson equation. We then use those results to locate the transition temperatures of both models in our Langevin dynamics simulations. We show that our results reconcile previous contradictory numerical works concerning the superroughening transition in the random sine-Gordon model. We also find evidence supporting the existence of two different low temperature phases for the disordered model. We discuss our results in view of the different analytical predictions available and comment on the nature of these two putative phases. We will also comment on the latest developments and results specifically about relaxation following a quench and the effects of a driving.