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Fractal to Nonfractal Phase Transition in the Dielectric Breakdown Model

M. B. Hastings
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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 $η_c=4$, at which a transition occurs between branching fractal clusters and one-dimensional nonfractal clusters.

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M. B. Hastings. 2001-06-01. Fractal to Nonfractal Phase Transition in the Dielectric Breakdown Model. https://doi.org/10.1103/physrevlett.87.175502

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