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Distribution of Dangling Ends on the Incipient Percolation Cluster

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arxiv cond-mat/9904152 v1 pith:PFQPDABA submitted 1999-04-12 cond-mat.stat-mech

Markus Porto , Armin Bunde , Shlomo Havlin This is my paper · ORCID
classification cond-mat.stat-mech
keywords clusterargumentsdanglingincipientpercolationscalingagreementbackbone
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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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