Conserved Kardar-Parisi-Zhang equation: Role of quenched disorder in determining universality

TL;DR

This paper investigates how quenched disorder affects the universality classes of the conserved KPZ equation, revealing relevance in one dimension and negligible impact at higher dimensions unless the disorder is long-ranged.

Contribution

It demonstrates that short-ranged quenched disorder induces a new universality class in one dimension, while at higher dimensions the effect depends on the disorder's range.

Findings

Short-ranged quenched disorder is relevant in 1D, creating a new universality class.

At higher dimensions, quenched disorder does not affect universal scaling unless long-ranged.

Long-ranged quenched disorder influences universality across all dimensions.

Abstract

We study the stochastically driven conserved Kardar-Parisi-Zhang (CKPZ) equation with quenched disorders. Short-ranged quenched disorders is found to be a relevant perturbation on the pure CKPZ equation at one dimension, and as a result, a new universality class different from pure CKPZ equation appears to emerge. At higher dimensions, quenched disorder turns out to be ineffective to influence the universal scaling. This results in the asymptotic long wavelength scaling to be given by the linear theory, a scenario identical with the pure CKPZ equation. For sufficiently long-ranged quenched disorders, the universal scaling is impacted by the quenched disorder even at higher dimensions.