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Exact Enumeration and Scaling for Fragmentation of PercolationClusters

Document Type

Conference Paper

Journal/Book Title/Conference

Bulletin of the American Physical Society



Publication Date



The fragmentation properties of percolation clusters yield information about their structure. Monte Carlo simulations and exact cluster enumeration for a square bond lattice and exact calculations for the Bethe lattice are used to study the fragmentation probability as(p) of clusters of mass s at an occupation probability p and the likelihood bs's(p) that fragmentation of an s cluster will result in a daughter cluster of mass s′. Evidence is presented to support the scaling laws as(pc)∼s and bs's(pc)=s−φg(s′/s), with φ=2-σ given by the standard cluster-number scaling exponent σ. Simulations for d=2 verify the finite-size-scaling form cs'sL(pc)=s1−φg̃(s′/s,s/Ldf) of the product cs's(pc)=as(pc)bs's(pc), where L is the lattice size and df is the fractal dimension. Exact calculations of the fragmentation probability fst of a cluster of mass s and perimeter t indicate that branches are important even on the maximum perimeter clusters. These calculations also show that the minimum of bs's(p) near s′=s/2, where the two daughter masses are comparable, deepens with increasing p.


Bull. Am. Phys. Soc. 37, 687

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