Europhys. Lett.
Volume 66, Number 4, May 2004
Page(s) 552 - 558
Section Condensed matter: structure, mechanical and thermal properties
Published online 01 May 2004
Europhys. Lett., 66 (4) , pp. 552-558 (2004)
DOI: 10.1209/epl/i2004-10021-1

Super-roughening as a disorder-dominated flat phase

S. Ares1, A. Sánchez1 and A. R. Bishop2

1  Grupo Interdisciplinar de Sistemas Complejos (GISC) ( and Departamento de Matemáticas, Universidad Carlos III de Madrid Avenida de la Universidad 30, 28911 Leganés, Madrid, Spain
2  Theoretical Division and Center for Nonlinear Studies, MS B258 Los Alamos National Laboratory, Los Alamos, NM 87545, USA

(Received 5 January 2004; accepted in final form 25 March 2004)

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 (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.

68.35.Ct - Interface structure and roughness.
68.35.Rh - Phase transitions and critical phenomena.
05.40.-a - Fluctuation phenomena, random processes, noise, and Brownian motion.

© EDP Sciences 2004