All Physics Faculty Publications

Document Type

Article

Journal/Book Title/Conference

Physical Review A

Volume

46

Issue

10

Publisher

American Physical Society

Publication Date

11-1-1992

First Page

6252

Last Page

6264

DOI

10.1103/PhysRevA.46.6252

Abstract

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)=sg(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.

Comments

http://pra.aps.org/abstract/PRA/v46/i10/p6252_1

Published by the American Physical Society in Physical Review A. Publisher PDF is available for download through the link above.