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

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 β = 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 the KPZ one. We associate the previously reported discrepancy with 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.