On the existence of an upper critical dimension for systems within the KPZ universality class

TL;DR

This paper extends the etching model to higher dimensions to investigate the existence of an upper critical dimension for the KPZ universality class, finding evidence that suggests it is not at four dimensions.

Contribution

It introduces a higher-dimensional extension of the etching model to analyze critical behavior in the KPZ class.

Findings

No evidence of an upper critical dimension at d=4

The exponents' behavior persists beyond four dimensions

Supports the non-existence of an upper critical dimension at four

Abstract

In this work we extend the etching model to $d+1$ dimensions. This permits us to investigate its exponents behaviour on higher dimensions, to try to verify the existence of an upper critical dimension for the KPZ equations, with our results sugesting that $d=4$ is not an upper critical dimension for the etching model.