Fractal to Nonfractal Phase Transition in the Dielectric Breakdown Model

Abstract

A fast method is presented for simulating the dielectric-breakdown model using iterated conformal mappings. Numerical results for the dimension and for corrections to scaling are in good agreement with the recent RG prediction of an upper critical ${\eta }_c=4$, at which a transition occurs between branching fractal clusters and one-dimensional nonfractal clusters.

5 pages, 7 figures; corrections to scaling included

References in corpus (1)

• Growth Exponents with 3.99 Walkers

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