TY - JOUR
T1 - The chemical distance distribution in percolation clusters
AU - Havlin, Shlomo
AU - Trus, Benes
AU - Weiss, George H.
AU - Ben-Avraham, Daniel
PY - 1985/4/1
Y1 - 1985/4/1
N2 - We study the conditional probability density p (r/l), for the geometrical distance r corresponding to a given chemical distance l for percolation clusters in two dimensions. We argue that (i) p(r/l) = A1xg exp(-axδ) where x = r/lv, g = 2.5 ± 0.3, δ = 9.8 ± 0.5, and v = 0.88 ± 0.02, and (ii) there is a relation δ = (l - v)-1 which is in good agreement with our numerical data. These results are derived by considering a special class of self-avoiding walks consisting of chains which are chemical paths (shortest paths) on critical percolation clusters.
AB - We study the conditional probability density p (r/l), for the geometrical distance r corresponding to a given chemical distance l for percolation clusters in two dimensions. We argue that (i) p(r/l) = A1xg exp(-axδ) where x = r/lv, g = 2.5 ± 0.3, δ = 9.8 ± 0.5, and v = 0.88 ± 0.02, and (ii) there is a relation δ = (l - v)-1 which is in good agreement with our numerical data. These results are derived by considering a special class of self-avoiding walks consisting of chains which are chemical paths (shortest paths) on critical percolation clusters.
UR - http://www.scopus.com/inward/record.url?scp=0002458123&partnerID=8YFLogxK
U2 - 10.1088/0305-4470/18/5/004
DO - 10.1088/0305-4470/18/5/004
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AN - SCOPUS:0002458123
SN - 0305-4470
VL - 18
SP - L247-L249
JO - Journal of Physics A: Mathematical and General
JF - Journal of Physics A: Mathematical and General
IS - 5
ER -