Fractal to nonfractal phase transition in the dielectric breakdown model.
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.
Hastings
M B
MB
CNLS, MS B258, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA. hastings@cnls.lanl.gov