Universality at the three-dimensional percolation threshold

D. Stauffer; J. Adler; A. Aharony

doi:10.1088/0305-4470/27/13/003

Universality at the three-dimensional percolation threshold

D. Stauffer, J. Adler, A. Aharony

Department of Physics

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43 Scopus citations

Abstract

The fraction of samples spanning a lattice at its percolation threshold is found via simulations of bond and site-bond percolation to have a universal value of about 0.42 in three dimensions. The ratio of shift (of the finite to infinite size threshold) to width of the threshold distribution is also compatible with universality. Lattices with up to 1001³ sites and/or very good statistics were needed to obtain clear results in these Monte Carlo tests; preliminary studies with smaller lattices were inconclusive.

Original language	English
Article number	003
Pages (from-to)	L475-L480
Journal	Journal of Physics A: Mathematical and General
Volume	27
Issue number	13
DOIs	https://doi.org/10.1088/0305-4470/27/13/003
State	Published - 1 Dec 1994

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
General Physics and Astronomy

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abstract = "The fraction of samples spanning a lattice at its percolation threshold is found via simulations of bond and site-bond percolation to have a universal value of about 0.42 in three dimensions. The ratio of shift (of the finite to infinite size threshold) to width of the threshold distribution is also compatible with universality. Lattices with up to 10013 sites and/or very good statistics were needed to obtain clear results in these Monte Carlo tests; preliminary studies with smaller lattices were inconclusive.",

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N2 - The fraction of samples spanning a lattice at its percolation threshold is found via simulations of bond and site-bond percolation to have a universal value of about 0.42 in three dimensions. The ratio of shift (of the finite to infinite size threshold) to width of the threshold distribution is also compatible with universality. Lattices with up to 10013 sites and/or very good statistics were needed to obtain clear results in these Monte Carlo tests; preliminary studies with smaller lattices were inconclusive.

AB - The fraction of samples spanning a lattice at its percolation threshold is found via simulations of bond and site-bond percolation to have a universal value of about 0.42 in three dimensions. The ratio of shift (of the finite to infinite size threshold) to width of the threshold distribution is also compatible with universality. Lattices with up to 10013 sites and/or very good statistics were needed to obtain clear results in these Monte Carlo tests; preliminary studies with smaller lattices were inconclusive.

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Universality at the three-dimensional percolation threshold

Abstract

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