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Fractal to nonfractal phase transition in the dielectric breakdown model
1CNLS, MS B258, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA. hastings@cnls.lanl.gov
Physical Review Letters
|November 3, 2001
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 renormalization group prediction of an upper critical eta(c) = 4, at which a transition occurs between branching fractal clusters and one-dimensional nonfractal clusters.