Fractal to Nonfractal Phase Transition in the Dielectric Breakdown Model

Details Fractal to Nonfractal Phase Transition in the Dielectric Breakdown Model Fractal to Nonfractal Phase Transition in the Dielectric Breakdown Model

2001-03-14

arxiv.org/abs/cond-mat/0103312v2

Phys. Rev. Lett. 87, 175502 (2001).

Physics

Condensed Matter

Soft Condensed Matter

5 pages, 7 figures; corrections to scaling included

Scientific paper

10.1103/PhysRevLett.87.175502

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.

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