TY - JOUR

T1 - Topological properties of percolation clusters

AU - Havlin, S.

AU - Nossal, R.

PY - 1984

Y1 - 1984

N2 - Percolation properties, including the total cluster mass S, the shell mass B, and the linear geometrical size R, are studied as a function of the topological 'chemical distance' parameter L. All critical exponents are shown to be related to an apparently new exponent nu , defined by R approximately L v. Critical exponents are calculated exactly for percolation clusters on the Cayley tree (a model for 6D percolation), for which S approximately L2, B approximately L, and R2 approximately L. For diffusion on such clusters one finds that L3 approximately t. Numerical estimates of the exponents are obtained for other dimensions. A conjecture which relates nu to beta and nu is discussed.

AB - Percolation properties, including the total cluster mass S, the shell mass B, and the linear geometrical size R, are studied as a function of the topological 'chemical distance' parameter L. All critical exponents are shown to be related to an apparently new exponent nu , defined by R approximately L v. Critical exponents are calculated exactly for percolation clusters on the Cayley tree (a model for 6D percolation), for which S approximately L2, B approximately L, and R2 approximately L. For diffusion on such clusters one finds that L3 approximately t. Numerical estimates of the exponents are obtained for other dimensions. A conjecture which relates nu to beta and nu is discussed.

UR - http://www.scopus.com/inward/record.url?scp=0000640467&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/17/8/007

DO - 10.1088/0305-4470/17/8/007

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AN - SCOPUS:0000640467

SN - 1751-8113

VL - 17

SP - L427-L432

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 8

M1 - 007

ER -