Super-roughening as a disorder-dominated flat phase

We study the phenomenon of super-roughening found on surfaces growing on disordered substrates. We consider a one-dimensional version of the problem for which the pure, ordered model exhibits a roughening phase transition. Extensive numerical simulations combined with analytical approximations indicate that super-roughening is a regime of asymptotically flat surfaces with non-trivial, rough short-scale features arising from the competition between surface tension and disorder. Based on this evidence and on previous simulations of the two-dimensional random sine-Gordon model (S´anchez et al., Phys. Rev. E, 62 (2000) 3219), we argue that this scenario is general and explains equally well the hitherto poorly understood two-dimensional case.This work has been supported by the Ministerio de Ciencia y Tecnolog´ıa of Spain through grants BFM2000-0006 and BFM2003-07749-C05-01 (SA and AS). Work at Los Alamos is performed under the auspices of the US Department of EnergyPublicad