Eur. Phys. J. B (2016) 89: 189
https://doi.org/10.1140/epjb/e2016-70132-5

Regular Article

On the origin of multiscaling in stochastic-field models of surface growth

¹ Departamento de Matemáticas, Universidad de Oviedo, Campus de Gijón, 33203 Gijón, Spain
² Grupo Interdisciplinar de Sistemas Complejos (GISC) and Grupo de Dinámica No Lineal (DNL), Escuela Técnica Superior de Ingeniería (ICAI), Universidad Pontificia Comillas, 28015 Madrid, Spain
³ Instituto de Física de Cantabria (IFCA), CSIC–UC, 39005 Santander, Spain

^a e-mail: rgallego@uniovi.es

Received: 3 March 2016
Received in final form: 9 June 2016
Published online: 5 September 2016

Abstract

Multiscaling appears in some non-equilibrium systems when different moments of a bulk averaged state variable scale with different and nontrivial exponents. This multiexponent scaling behaviour is highly nontrivial and is associated with different fractal properties at different observation scales. It is unclear what kind of generic mechanisms could make multiscaling to emerge in continuous hydrodynamic descriptions of dynamical systems with only local interactions, governed by partial-differential equations, in the continuum. Here we present an extensive numerical study of a continuous model of epitaxial thin-film growth, which main characteristic is that it includes infinitely many nonlinearities. For strong enough nonlinearity, the model shows effective multiscaling over a range of time/length scales, while normal monoscaling is actually recovered at long wavelengths. We conjecture that the existence of infinitely many weakly relevant nonlinear terms may lead to this nontrivial scaling behaviour in a generic way.