Detailed results are reported for the connectivity properties of a system of discs of unit radius free to be situated anywhere within a square of area 2L2. Ordinary lattice percolation would correspond to the discs being situated on the vertices of a square root 2L* square root 2L lattice. Computer simulations are carried out for a sequence of increasing system sizes ranging from L=20 to L=1000; for each value of L a large number of realisations are generated for 25 values of the disc concentration x. The authors calculate a variety of estimates for the threshold parameter xc, as well as the critical exponents beta , gamma , tau , and nu . Their exponent estimates are in close agreement with accepted values for ordinary lattice percolation, therefore this continuum system appears to be in the same 'universality class' as lattice percolation.
%0 Journal Article
%1 Gawlinski1981Continuum
%A Gawlinski, E. T.
%A Stanley, H. E.
%D 1981
%J Journal of Physics A: Mathematical and General
%K montecarlo, scaling percolation
%N 8
%P L291--L299
%R 10.1088/0305-4470/14/8/007
%T Continuum percolation in two dimensions: Monte Carlo tests of scaling and universality for non-interacting discs
%U http://dx.doi.org/10.1088/0305-4470/14/8/007
%V 14
%X Detailed results are reported for the connectivity properties of a system of discs of unit radius free to be situated anywhere within a square of area 2L2. Ordinary lattice percolation would correspond to the discs being situated on the vertices of a square root 2L* square root 2L lattice. Computer simulations are carried out for a sequence of increasing system sizes ranging from L=20 to L=1000; for each value of L a large number of realisations are generated for 25 values of the disc concentration x. The authors calculate a variety of estimates for the threshold parameter xc, as well as the critical exponents beta , gamma , tau , and nu . Their exponent estimates are in close agreement with accepted values for ordinary lattice percolation, therefore this continuum system appears to be in the same 'universality class' as lattice percolation.
@article{Gawlinski1981Continuum,
abstract = {{Detailed results are reported for the connectivity properties of a system of discs of unit radius free to be situated anywhere within a square of area 2L2. Ordinary lattice percolation would correspond to the discs being situated on the vertices of a square root 2L* square root 2L lattice. Computer simulations are carried out for a sequence of increasing system sizes ranging from L=20 to L=1000; for each value of L a large number of realisations are generated for 25 values of the disc concentration x. The authors calculate a variety of estimates for the threshold parameter xc, as well as the critical exponents beta , gamma , tau , and nu . Their exponent estimates are in close agreement with accepted values for ordinary lattice percolation, therefore this continuum system appears to be in the same 'universality class' as lattice percolation.}},
added-at = {2019-06-10T14:53:09.000+0200},
author = {Gawlinski, E. T. and Stanley, H. E.},
biburl = {https://www.bibsonomy.org/bibtex/2e2a306667f1517b4cab059ecc970648a/nonancourt},
citeulike-article-id = {4168648},
citeulike-linkout-0 = {http://dx.doi.org/10.1088/0305-4470/14/8/007},
doi = {10.1088/0305-4470/14/8/007},
interhash = {f99c0c547334776dea1f72296c8cda33},
intrahash = {e2a306667f1517b4cab059ecc970648a},
journal = {Journal of Physics A: Mathematical and General},
keywords = {montecarlo, scaling percolation},
number = 8,
pages = {L291--L299},
posted-at = {2009-03-12 15:38:10},
priority = {2},
timestamp = {2019-07-31T12:25:48.000+0200},
title = {{Continuum percolation in two dimensions: Monte Carlo tests of scaling and universality for non-interacting discs}},
url = {http://dx.doi.org/10.1088/0305-4470/14/8/007},
volume = 14,
year = 1981
}