title: Percolation transitions with nonlocal constraint.
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 nonpercolating phase to a quasicritical phase where the largest cluster size G scales as G~N(α) with α=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.
authors.affiliation: Department of Physics, University of Seoul, Seoul 130-743, Korea.
authors.forename: Pyoung-Seop
authors.initials: PS
authors.lastname: Shim
authors.forename: Hyun Keun
authors.initials: HK
authors.lastname: Lee
authors.forename: Jae Dong
authors.initials: JD
authors.lastname: Noh