Scaling of the active zone in the Eden process on percolation networks and the ballistic deposition model

TLDR

Monte Carlo simulations were used to study the interface of Eden clusters on percolation networks and the ballistic deposition model, defining surface thickness simply. The study found that in ballistic deposition the active‑zone width diverges differently from the mean height, violating the single‑scaling‑length assumption, while in Eden clusters on percolation networks the exponents for radius and active‑zone divergence are essentially equal (with ν′ slightly smaller than ν), and ballistic deposits exhibit finite‑size scaling of surface thickness.

Abstract

The interface of the Eden clusters on percolation networks and the ballistic deposition model is studied by Monte Carlo simulations, using a simple definition for the surface thickness. The width of the active zone in the ballistic deposition model is found to diverge differently from the mean height, indicating breakdown of the single scaling length assumption in this model. The exponents nu and nu ' describing, respectively, the divergence of the radius and the active zone of the Eden clusters on percolation networks appear to be the same within the statistical errors. The central value of nu ', however, is slightly, but systematically, less than nu . The surface thickness of ballistic deposits is shown to exhibit finite-size scaling.