Physical Sciences and Mathematics Commons^™

Exact Enumeration And Scaling For Fragmentation Of Percolation Clusters, Boyd F. Edwards, M. F. Gyure, M. V. Ferer

All Physics Faculty Publications

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 …