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 ηc=4, at which a transition occurs between branching fractal clusters and one-dimensional nonfractal clusters.
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