Growth exponents of the etching model in high dimensions

Abstract

In this work we generalize the etching model (Mello et al 2001 Phys. Rev. E 63 041113) to d + 1 dimensions. The dynamic exponents of this model are compatible with those of the Kardar–Parisi–Zhang universality class. We investigate the roughness dynamics with surfaces up to d = 6. We show that the data from all substrate lengths and for all dimensions can be collapsed into one common curve. We determine the dynamic exponents as a function of the dimension. Moreover, our results suggest that d = 4 is not an upper critical dimension for the etching model, and that it fulfills the Galilean invariance.