title: Continuity of the explosive percolation transition.
abstract: The explosive percolation problem on the complete graph is investigated via extensive numerical simulations. We obtain the cluster-size distribution at the moment when the cluster size heterogeneity becomes maximum. The distribution is found to be well described by the power-law form with the decay exponent τ=2.06(2), followed by a hump. We then use the finite-size scaling method to make all the distributions at various system sizes up to N=2(37) collapse perfectly onto a scaling curve characterized solely by the single exponent τ. We also observe that the instant of that collapse converges to a well-defined percolation threshold from below as N→∞. Based on these observations, we show that the explosive percolation transition in the model should be continuous, contrary to the widely spread belief of its discontinuity.
authors.affiliation: Department of Physics, University of Seoul, Seoul 130-743, Korea.
authors.forename: Hyun Keun
authors.initials: HK
authors.lastname: Lee
authors.forename: Beom Jun
authors.initials: BJ
authors.lastname: Kim
authors.forename: Hyunggyu
authors.initials: H
authors.lastname: Park