2006/11/06 by Leticia R. Paiva, L. R. Paiva, Silvio C. Ferreira +1 · 1 citation
Mathematics · Physics and Astronomy · #Anisotropy #Condensed matter physics #Exponent #Geometry #Isotropy #Lattice (music) #Lattice plane #Mathematical physics #Mathematics #Physics #Power law #Quantum mechanics #Random Matrices and Applications #Reciprocal lattice #Renormalization group #Scaling #Statistical physics #Statistics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Universality (dynamical systems) #cond-mat.stat-mech
paper · pdf · doi:10.1088/1751-8113/40/1/f05
published as J. Phys. A: Math. Theor. 40 F43 2007 · To appear in J. Phys. A: Math. Gen
arxiv created 2006/11/06 · openalex publication_date 2006/12/06 · arxiv updated 2011/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 neighbors. Large scale simulations (N\gtrsim 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 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.