Super-roughening as a disorder-dominated flat phase

TL;DR

This paper investigates super-roughening in disordered surface growth, revealing it as a regime of asymptotically flat surfaces with complex local features, supported by simulations and analytical methods, and extends the understanding to two dimensions.

Contribution

It provides a new interpretation of super-roughening as a disorder-dominated flat phase, supported by numerical and analytical evidence, and generalizes findings to higher dimensions.

Findings

Super-roughening surfaces are asymptotically flat with local rough features.

Numerical simulations and analytical approximations support the disorder-dominated flat phase scenario.

The results extend to two-dimensional models, explaining previous observations.

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 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 [Sanchez 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.