Super-roughening as a disorder-dominated flat phase

PACS. 68.35.Ct – Interface structure and roughness. PACS. 68.35.Rh – Phase transitions and critical phenomena. PACS. 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion. Abstract. – 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 asymp-totically 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 (Sánchez 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. Understanding phase transitions in systems with quenched disorder is a challenging issue, not only in physics but also in fields ranging from combinatorics to financial market mod-eling. This is the reason why much effort has been devoted in the last few years to thi