%0 Journal Article %1 Shim2012Percolation %A Shim, Pyoung-Seop %A Lee, Hyun %A Noh, Jae %D 2012 %J Physical Review E %K nonlocality, percolation critical-phenomena %N 3 %R 10.1103/PhysRevE.86.031113 %T Percolation transitions with nonlocal constraint %U http://dx.doi.org/10.1103/PhysRevE.86.031113 %V 86 %X We investigate percolation transitions in a nonlocal network model numerically. In this model, each node has an exclusive partner and a link is forbidden between two nodes whose \$r\$-neighbors share any exclusive pair. The \$r\$-neighbor of a node \$x\$ is defined as a set of at most \$N^r\$ neighbors of \$x\$, where \$N\$ is the total number of nodes. The parameter \$r\$ controls the strength of a nonlocal effect. The system is found to undergo a percolation transition belonging to the mean field universality class for \$r< 1/2\$. On the other hand, for \$r>1/2\$, the system undergoes a peculiar phase transition from a non-percolating phase to a quasi-critical phase where the largest cluster size \$G\$ scales as \$G N^\alpha\$ with \$= 0.74 (1)\$. In the marginal case with \$r=1/2\$, the model displays a percolation transition that does not belong to the mean field universality class.

@article{Shim2012Percolation, abstract = {We investigate percolation transitions in a nonlocal network model numerically. In this model, each node has an exclusive partner and a link is forbidden between two nodes whose \$r\$-neighbors share any exclusive pair. The \$r\$-neighbor of a node \$x\$ is defined as a set of at most \$N^r\$ neighbors of \$x\$, where \$N\$ is the total number of nodes. The parameter \$r\$ controls the strength of a nonlocal effect. The system is found to undergo a percolation transition belonging to the mean field universality class for \$r< 1/2\$. On the other hand, for \$r>1/2\$, the system undergoes a peculiar phase transition from a non-percolating phase to a quasi-critical phase where the largest cluster size \$G\$ scales as \$G \sim N^{\alpha}\$ with \$\alpha = 0.74 (1)\$. In the marginal case with \$r=1/2\$, the model displays a percolation transition that does not belong to the mean field universality class.}, added-at = {2019-06-10T14:53:09.000+0200}, archiveprefix = {arXiv}, author = {Shim, Pyoung-Seop and Lee, Hyun and Noh, Jae}, biburl = {https://www.bibsonomy.org/bibtex/296b68e27db90e8c18265d9f491a480a4/nonancourt}, citeulike-article-id = {10714068}, citeulike-linkout-0 = {http://dx.doi.org/10.1103/PhysRevE.86.031113}, citeulike-linkout-1 = {http://arxiv.org/abs/1205.5884}, citeulike-linkout-2 = {http://arxiv.org/pdf/1205.5884}, day = 26, doi = {10.1103/PhysRevE.86.031113}, eprint = {1205.5884}, interhash = {aa718b6412fa5a44d868ff5fa235977f}, intrahash = {96b68e27db90e8c18265d9f491a480a4}, issn = {1550-2376}, journal = {Physical Review E}, keywords = {nonlocality, percolation critical-phenomena}, month = sep, number = 3, posted-at = {2012-05-29 12:24:23}, priority = {2}, timestamp = {2019-07-31T12:26:23.000+0200}, title = {{Percolation transitions with nonlocal constraint}}, url = {http://dx.doi.org/10.1103/PhysRevE.86.031113}, volume = 86, year = 2012 }