Spanning lengths of percolation clusters

descriptionPublicationkeyboard_double_arrow_right Article 01 Jul 1978 English Publisher:Springer Science and Business Media LLCJournal:Journal of Statistical Physics, volume 19, pages 53-64 (issn: 0022-4715, eissn: 1572-9613,

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Authors: Ralph J. Harrison; George H. Bishop; George D. Quinn;

doi: 10.1007/bf01020333

Spanning lengths of percolation clusters

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Abstract

The spanning length of a percolation cluster is defined as the difference between the maximum and minimum coordinates of the cluster with respect to some chosen direction. It is statistically related to the number size of the cluster by an exponent that differs from the iriverse dimension that would characterize a compact cluster. This exponent for large percolation clusters in simple cubic lattice sites was studied by the Monte Carlo technique, and results are presented. Previous theoretical treatments of this exponent and its relationship with other critical exponents are discussed.

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