Eden clusters in three-dimensions and the Kardar-Parisi-Zhang universality class

TL;DR

This paper demonstrates through large-scale simulations that three-dimensional radial Eden clusters belong to the KPZ universality class, confirming the growth exponent and addressing previous discrepancies in the literature.

Contribution

The study provides conclusive simulation evidence that 3D radial Eden growth aligns with KPZ universality, refuting prior claims of a different universality class.

Findings

Growth exponent matches the KPZ value of 0.242

Radial Eden growth in 3D belongs to KPZ universality class

Skewness and kurtosis measured for flat 2+1D Eden clusters

Abstract

We present large-scale simulations of radial Eden clusters in three-dimensions and show that the growth exponent is in agreement with the value $\beta=0.242$ accepted for the Kardar-Parisi-Zhang (KPZ) universality class. Our results refute a recent assertion proposing that radial Eden growth in $d=3$ belongs to a universality class distinct from KPZ. We associate the previously reported discrepancy to a slow convergence to the asymptotic limit. We also present the skewness and kurtosis in the roughening regime for flat geometry in 2+1 dimensions.