Explosive percolation via control of the largest cluster.
We show that considering only the largest cluster suffices to obtain a first-order percolation transition. As opposed to previous realizations of explosive percolation, our models obtain Gaussian cluster distributions and compact clusters as one would expect at first-order transitions. We also discover that the cluster perimeters are fractal at the transition point, yielding a fractal dimension of 1.23 ± 0.03, close to that of watersheds.
Araújo
N A M
NA
Computational Physics for Engineering Materials, IfB, ETH Zurich, Schafmattstrasse 6, 8093 Zurich, Switzerland. nuno@ethz.ch
Herrmann
H J
HJ