%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 }