Universality class of isotropic on-lattice Eden clusters

TL;DR

This paper introduces an extended Eden model with a power-law growth probability to eliminate lattice anisotropy effects, revealing KPZ universality in on-lattice Eden clusters through large-scale simulations.

Contribution

The study demonstrates that adjusting growth probability in the Eden model can recover KPZ universality class behavior in on-lattice clusters.

Findings

Lattice anisotropy causes linear growth of interface width.

Proper power-law growth probability removes anisotropy effects.

Cluster growth aligns with KPZ universality class after modification.

Abstract

The shape of large on-lattice Eden clusters grown from a single seed is ruled by the underlying lattice anisotropy. This is reflected on the linear growth with time of the interface width ($w\sim t$), in contrast with the KPZ universality class ($w\sim t^{1/3}$) observed when the Eden model is grown on flat substrates. We propose an extended Eden model, in which the growth probability has a power law dependence with the number of occupied nearest neighbors. Large scale simulations ($N\gtrsim 4\times 10^9$ particles) were used to determine the time evolution of $w$. We found that a suitable choice of the power exponent removes the lattice-induced cluster anisotropy and provides a growth exponent in very good agreement with the KPZ universality class. Also, the present model corroborates the results found in off-lattice simulations, in which the center of mass fluctuations are considered in the interface scaling analysis.