Universality and Scale Invariant Dynamics in Laplacian Fractal Growth

Abstract

The individuation of the scale invariant dynamics in Laplacian fractal growth processes, like diffusion-limited aggregation (DLA), is an important problem whose solution would clarify some crucial issues concerning the origin of fractal properties and the identification of universality classes for such models. Here, we develop a real space renormalization group scheme to study the dynamic evolution of DLA in a restricted space of relevant parameters. In particular, we investigate the effect of a sticking probability P s and an effective noise reduction parameter S. The renormalization equations flow towards an attractive fixed point corresponding to the scale invariant DLA dynamics ([Formula: see text], S*≃2.0). The existence of a non-trivial fixed point value for S, shows that noise is spontaneously generated by the DLA growth process, and that screening, which is at the origin of fractal properties, persists at all scales.