Universality class of isotropic on-lattice Eden clusters

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 ∼ t), in contrast with the KPZ universality class (w ∼ t1/3) 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 neighbours. Large-scale simulations (N ≳ 4 × 109 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 a very good agreement with the KPZ universality class. Also, the present model corroborates the results found in off-lattice simulations, in which the centre-of-mass fluctuations are considered in the interface scaling analysis.