Exact Enumeration and Scaling for Fragmentation of Percolation Clusters

Authors

Boyd F. Edwards, Utah State UniversityFollow
M. F. Gyure
M. V. Ferer

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

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 a_s(p) of clusters of mass s at an occupation probability p and the likelihood b_s′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 a_s(p_c)∼s and b_s′s(p_c)=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 c_s′sL(p_c)=s^1-φg̃(s′/s,s/L^d_f) of the product c_s′s(p_c)=a_s(p_c)b_s′s(p_c), where L is the lattice size and d_f is the fractal dimension. Exact calculations of the fragmentation probability f_st 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 b_s′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.

Recommended Citation

Exact Enumeration and Scaling for Fragmentation of PercolationClusters, B. F. Edwards, M. F. Gyure, and M. V. Ferer, Phys. Rev. A,46, 6252 (1992) [15].