%0 Journal Article %1 Parisi2008Kcore %A Parisi, Giorgio %A Rizzo, Tommaso %D 2008 %J Physical Review E %K bethe\_lattice, percolation k-core %N 2 %R 10.1103/PhysRevE.78.022101 %T k-core percolation in four dimensions %U http://dx.doi.org/10.1103/PhysRevE.78.022101 %V 78 %X The \$k\$-core percolation on the Bethe lattice has been proposed as a simple model of the jamming transition because of its hybrid first-order/second-order nature. We investigate numerically \$k\$-core percolation on the four-dimensional regular lattice. For \$k=4\$ the presence of a discontinuous transition is clearly established but its nature is strictly first order. In particular, the \$k\$-core density displays no singular behavior before the jump and its correlation length remains finite. For \$k=3\$ the transition is continuous.

@article{Parisi2008Kcore, abstract = {{The \$k\$-core percolation on the Bethe lattice has been proposed as a simple model of the jamming transition because of its hybrid first-order/second-order nature. We investigate numerically \$k\$-core percolation on the four-dimensional regular lattice. For \$k=4\$ the presence of a discontinuous transition is clearly established but its nature is strictly first order. In particular, the \$k\$-core density displays no singular behavior before the jump and its correlation length remains finite. For \$k=3\$ the transition is continuous.}}, added-at = {2019-06-10T14:53:09.000+0200}, archiveprefix = {arXiv}, author = {Parisi, Giorgio and Rizzo, Tommaso}, biburl = {https://www.bibsonomy.org/bibtex/22ebf3c074648341fda68e5b49dc23964/nonancourt}, citeulike-article-id = {10512172}, citeulike-linkout-0 = {http://dx.doi.org/10.1103/PhysRevE.78.022101}, citeulike-linkout-1 = {http://arxiv.org/abs/cond-mat/0609777}, citeulike-linkout-2 = {http://arxiv.org/pdf/cond-mat/0609777}, day = 29, doi = {10.1103/PhysRevE.78.022101}, eprint = {cond-mat/0609777}, interhash = {093ce122d6b539e5a075c06d0fb5bfdf}, intrahash = {2ebf3c074648341fda68e5b49dc23964}, issn = {1550-2376}, journal = {Physical Review E}, keywords = {bethe\_lattice, percolation k-core}, month = aug, number = 2, posted-at = {2012-03-29 21:13:55}, priority = {2}, timestamp = {2019-08-01T16:09:09.000+0200}, title = {{k-core percolation in four dimensions}}, url = {http://dx.doi.org/10.1103/PhysRevE.78.022101}, volume = 78, year = 2008 }