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 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, 3219 (2000)], 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 this subject. However, the progress achieved so far is modest, and clear-cut, definitive results are rare [1]. In view of this, steps towards providing such results are needed and will be very helpful for many ongoing investigations. One important instance where the role of disorder remains unclear is that of roughening transitions of crystal surfaces [2]: At high temperatures, crystal surfaces are rough (the surface width w increases with the system size L), whereas at low temperatures they become flat (w is a constant depending only on temperature). When crystal planes are grown on a disordered substrate, renormalization group calculations for the two-dimensional (2D) random sine-Gordon model (RsGM, see below) predicted that the conventional roughening transition was replaced by super-roughening [3], a new phase transition from the high temperature rough phase (w ∼ √ ln L) to a low temperature rougher phase (w ∼ ln L). Subsequent work produced a " myriad of predictions " [4] in a few years, which gave rise to a controversy about the nature of the super-rough phase (see [5] for a review). Based mainly on large-scale numerical simulations or exact optimization results [6–14], some degree of consensus was reached that super-roughening indeed took place and that w ∼ ln L c EDP Sciences