Anomalous scaling in a non local growth model in the Kardar-Parisi-Zhang universality class

TL;DR

This paper investigates a discrete electrochemical deposition model, revealing initial instability and anomalous scaling behavior, ultimately aligning with the KPZ universality class, and highlighting different roughness exponents at various scales.

Contribution

It demonstrates that a non-local growth model exhibits anomalous scaling and aligns with KPZ universality, providing insights into electrochemical deposition dynamics.

Findings

Initial interface instability observed

Asymptotic KPZ scaling confirmed

Anomalous power spectrum at early times

Abstract

We study the interface dynamics of a discrete model to quantitatively describe electrochemical deposition experiments. Extensive numerical simulations indicate that the interface dynamics is unstable at early times, but asymptotically displays the scaling of the Kardar-Parisi-Zhang universality class. During the time interval in which the surface is unstable, its power spectrum is anomalous; hence the behaviors at length scales smaller than or comparable with the system size are described by different roughness exponents. These results are expected to apply to a wide range of electrochemical deposition experiments.