Bootstrap (or k-core) Percolation with k = 3 is studied numerically on two-dimensional lattices with long-range links whose lengths r ij are distributed according to P ( r ) \~ r −α . By varying the decay exponent α the topology of these networks can be made to range from two-dimensional short-range networks to ∞-dimensional random graphs. The 3-core transition is found to be of first-order character with a divergent correlation length for α < 2.75 and of second order for larger α . Whenever the transition is first-order an associated critical corona is found to exist. The correlation length exponent ν defined from the corona correlation length above the first order transition is estimated as v 1/2 for α = 0, and only shows a weak α dependence for α ≤ 2.50. The second-order transition at large α is found to be in the universality class of two-dimensional Percolation.
%0 Journal Article
%1 Moukarzel2010Longrange
%A Moukarzel, C. F.
%A Sokolowski, T.
%D 2010
%J Journal of Physics: Conference Series
%K phase\_transitions percolation k-core
%N 1
%P 012019+
%R 10.1088/1742-6596/246/1/012019
%T Long-range k-core percolation
%U http://dx.doi.org/10.1088/1742-6596/246/1/012019
%V 246
%X Bootstrap (or k-core) Percolation with k = 3 is studied numerically on two-dimensional lattices with long-range links whose lengths r ij are distributed according to P ( r ) \~ r −α . By varying the decay exponent α the topology of these networks can be made to range from two-dimensional short-range networks to ∞-dimensional random graphs. The 3-core transition is found to be of first-order character with a divergent correlation length for α < 2.75 and of second order for larger α . Whenever the transition is first-order an associated critical corona is found to exist. The correlation length exponent ν defined from the corona correlation length above the first order transition is estimated as v 1/2 for α = 0, and only shows a weak α dependence for α ≤ 2.50. The second-order transition at large α is found to be in the universality class of two-dimensional Percolation.
@article{Moukarzel2010Longrange,
abstract = {{Bootstrap (or k-core) Percolation with k = 3 is studied numerically on two-dimensional lattices with long-range links whose lengths r ij are distributed according to P ( r ) \~{} r −α . By varying the decay exponent α the topology of these networks can be made to range from two-dimensional short-range networks to ∞-dimensional random graphs. The 3-core transition is found to be of first-order character with a divergent correlation length for α < 2.75 and of second order for larger α . Whenever the transition is first-order an associated critical corona is found to exist. The correlation length exponent ν defined from the corona correlation length above the first order transition is estimated as v 1/2 for α = 0, and only shows a weak α dependence for α ≤ 2.50. The second-order transition at large α is found to be in the universality class of two-dimensional Percolation.}},
added-at = {2019-06-10T14:53:09.000+0200},
author = {Moukarzel, C. F. and Sokolowski, T.},
biburl = {https://www.bibsonomy.org/bibtex/2dfbfdef75308a9743427db6a58f8683e/nonancourt},
citeulike-article-id = {7876763},
citeulike-linkout-0 = {http://dx.doi.org/10.1088/1742-6596/246/1/012019},
citeulike-linkout-1 = {http://iopscience.iop.org/1742-6596/246/1/012019},
day = 1,
doi = {10.1088/1742-6596/246/1/012019},
interhash = {de5e0e05a2f842e027979c0f17a89429},
intrahash = {dfbfdef75308a9743427db6a58f8683e},
issn = {1742-6596},
journal = {Journal of Physics: Conference Series},
keywords = {phase\_transitions percolation k-core},
month = sep,
number = 1,
pages = {012019+},
posted-at = {2010-09-22 14:29:50},
priority = {2},
timestamp = {2019-08-01T16:09:09.000+0200},
title = {{Long-range k-core percolation}},
url = {http://dx.doi.org/10.1088/1742-6596/246/1/012019},
volume = 246,
year = 2010
}