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 $\beta =0.242$ 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.

arXiv comment5 pages, 4 figures, published at JSTAT

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• Non-universal parameters, corrections and universality in Kardar-Parisi-Zhang growth
• On the origins of scaling corrections in ballistic growth models
• Eden model with nonlocal growth rules and the kinetic roughening in biological systems
• Dynamical universality classes of simple growth and lattice gas models
• Hallmarks of the Kardar-Parisi-Zhang universality class elicited by scanning probe microscopy