Self similarity and correlations in percolation

A. Kapitulnik; A. Aharony; G. Deutscher; D. Stauffer

doi:10.1088/0305-4470/16/8/003

Self similarity and correlations in percolation

A. Kapitulnik^*, A. Aharony, G. Deutscher, D. Stauffer

^*Corresponding author for this work

School of Physics and Astronomy

Tel Aviv University

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142 Scopus citations

Abstract

The infinite cluster above the percolation threshold is shown by a scaling theory and Monte Carlo simulations to be homogeneous on large length scales (compared with the correlation length). On shorter length scales this cluster is self similar, and its measured fractal dimensionality agrees excellently with the scaling law D=d- beta / nu . The exponents beta and nu are also measured, both from the crossover between the two length scale regions and from correlations near the boundaries.

Original language	English
Article number	003
Pages (from-to)	L269-L274
Journal	Journal of Physics A: Mathematical and General
Volume	16
Issue number	8
DOIs	https://doi.org/10.1088/0305-4470/16/8/003
State	Published - 1983

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title = "Self similarity and correlations in percolation",

abstract = "The infinite cluster above the percolation threshold is shown by a scaling theory and Monte Carlo simulations to be homogeneous on large length scales (compared with the correlation length). On shorter length scales this cluster is self similar, and its measured fractal dimensionality agrees excellently with the scaling law D=d- beta / nu . The exponents beta and nu are also measured, both from the crossover between the two length scale regions and from correlations near the boundaries.",

author = "A. Kapitulnik and A. Aharony and G. Deutscher and D. Stauffer",

year = "1983",

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AU - Deutscher, G.

AU - Stauffer, D.

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Y1 - 1983

N2 - The infinite cluster above the percolation threshold is shown by a scaling theory and Monte Carlo simulations to be homogeneous on large length scales (compared with the correlation length). On shorter length scales this cluster is self similar, and its measured fractal dimensionality agrees excellently with the scaling law D=d- beta / nu . The exponents beta and nu are also measured, both from the crossover between the two length scale regions and from correlations near the boundaries.

AB - The infinite cluster above the percolation threshold is shown by a scaling theory and Monte Carlo simulations to be homogeneous on large length scales (compared with the correlation length). On shorter length scales this cluster is self similar, and its measured fractal dimensionality agrees excellently with the scaling law D=d- beta / nu . The exponents beta and nu are also measured, both from the crossover between the two length scale regions and from correlations near the boundaries.

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Self similarity and correlations in percolation

Abstract

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