Continuity of the explosive percolation transition

被引:84
作者
Lee, Hyun Keun [1 ,2 ]
Kim, Beom Jun [2 ]
Park, Hyunggyu [3 ]
机构
[1] Univ Seoul, Dept Phys, Seoul 130743, South Korea
[2] Sungkyunkwan Univ, Phys Res Div BK21, Suwon 440746, South Korea
[3] Korea Inst Adv Study, Sch Phys, Seoul 130722, South Korea
来源
PHYSICAL REVIEW E | 2011年 / 84卷 / 02期
关键词
D O I
10.1103/PhysRevE.84.020101
中图分类号
O35 [流体力学]; O53 [等离子体物理学];
学科分类号
070204 ; 080103 ; 080704 ;
摘要
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 tau = 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 tau. We also observe that the instant of that collapse converges to a well-defined percolation threshold from below as N -> infinity. 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.
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页数:4
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