The crossover phenomena in surface growth models with height-dependent noise

Abstract

In this paper, we consider several known growth processes with height-dependent noise. This type of noise is interesting from a theoretical standpoint, for example, it paves the way to the derivation of the exact height distribution of the KPZ equation through the Hopf–Cole transformation. In addition, it may have implications for experimental growth processes. Using numerical methods, we observe that adding such a noise to different growth processes, can change their universality class or ruin the scaling laws. In the case of Mullins–Herring equation, a two-fold cross-over is observed.