Growth exponents of the etching model in high dimensions

TL;DR

This paper extends the etching model to higher dimensions, analyzing its dynamic exponents and universality class, and finds that the model's behavior is consistent across dimensions up to six, with no upper critical dimension at four.

Contribution

The study generalizes the etching model to d+1 dimensions and investigates its dynamic exponents, revealing its compatibility with the KPZ universality class and challenging previous assumptions about the upper critical dimension.

Findings

Dynamic exponents match KPZ universality class.

Data collapses onto a single curve across dimensions.

No upper critical dimension at d=4 for the model.

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.