Distribution of Dangling Ends on the Incipient Percolation Cluster

Details Distribution of Dangling Ends on the Incipient Percolation Cluster Distribution of Dangling Ends on the Incipient Percolation Cluster

1999-04-12

arxiv.org/abs/cond-mat/9904152v1

Physics

Condensed Matter

Statistical Mechanics

proceedings of the conference "Percolation and Disordered Systems: *Theory and Applications*", Giessen (Germany) 1998, see h

Scientific paper

We study numerically and by scaling arguments the probability P(M)dM that a given dangling end of the incipient percolation cluster has a mass between M and M + dM. We find by scaling arguments that P(M) decays with a power law, P(M)~M^(-(1+k)), with an exponent k=dBf/df, where df and dBf are the fractal dimensions of the cluster and its backbone, respectively. Our numerical results yield k=0.83 in d=2 and k=0.74 in d=3 in very good agreement with theory.

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