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-φg(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. © 1992 The American Physical Society.
CITATION STYLE
Edwards, B. F., Gyure, M. F., & Ferer, M. (1992). Exact enumeration and scaling for fragmentation of percolation clusters. Physical Review A, 46(10), 6252–6264. https://doi.org/10.1103/PhysRevA.46.6252
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