Universality of fluctuations in the Kardar-Parisi-Zhang class in high dimensions and its upper critical dimension

TL;DR

This study demonstrates that the KPZ class's fluctuation behavior remains universal up to six dimensions and suggests that its upper critical dimension is infinite, based on analysis of the RSOS model.

Contribution

It extends the understanding of KPZ universality to higher dimensions and proposes that the upper critical dimension is infinite.

Findings

Height distributions are universal up to d=6.

Fluctuations remain significant at d=6.

Upper critical dimension of KPZ is likely infinite.

Abstract

We show that the theoretical machinery developed for the Kardar-Parisi-Zhang (KPZ) class in low dimensions are obeyed by the restricted solid-on-solid (RSOS) model for substrates with dimensions up to $d=6$. Analyzing different restriction conditions, we show that height distributions of the interface are universal for all investigated dimensions. It means that fluctuations are not negligible and, consequently, the system is still below the upper critical dimension at $d=6$. The extrapolation of the data to dimensions $d\ge7$ predicts that the upper critical dimension of the KPZ class is infinite.