High dimensional behavior of the Kardar-Parisi-Zhang growth dynamics

TL;DR

This paper analyzes the behavior of KPZ surface growth in high dimensions, revealing that the roughness exponent decreases as 1/d and suggesting there is no finite upper critical dimension for this dynamics.

Contribution

It provides an analytical study of KPZ growth in high dimensions using a non-perturbative renormalization approach, showing the decay of the roughness exponent and the absence of an upper critical dimension.

Findings

Roughness exponent $eta$ decays as 1/d for large d

No finite upper critical dimension exists for KPZ dynamics

Analytical framework used is a non-perturbative renormalization method

Abstract

We investigate analytically the large dimensional behavior of the Kardar-Parisi-Zhang (KPZ) dynamics of surface growth using a recently proposed non-perturbative renormalization for self-affine surface dynamics. Within this framework, we show that the roughness exponent $\alpha$ decays not faster than $\alpha\sim 1/d$ for large $d$. This implies the absence of a finite upper critical dimension.