title: Roughening and super-roughening in the ordered and random two-dimensional sine-gordon models
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 super-roughening 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.
authors.affiliation: Grupo Interdisciplinar de Sistemas Complicados (GISC), Departamento de Matematicas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganes, Madrid, Spain.
authors.initials: A
authors.lastname: Sanchez
authors.initials: AR
authors.lastname: Bishop
authors.initials: E
authors.lastname: Moro