Explosive Percolation Transition is Actually Continuous
نویسندگان
چکیده
منابع مشابه
Explosive percolation is continuous, but with unusual finite size behavior.
We study four Achlioptas-type processes with "explosive" percolation transitions. All transitions are clearly continuous, but their finite size scaling functions are not entirely holomorphic. The distributions of the order parameter, i.e., the relative size s(max)/N of the largest cluster, are double humped. But-in contrast to first-order phase transitions-the distance between the two peaks dec...
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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 th...
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In this Letter, we show that the explosive percolation is a novel continuous phase transition. The order-parameter-distribution histogram at the percolation threshold is studied in Erd˝ os-Rényi networks, scale-free networks, and square lattice. In finite system, two well-defined Gaussian-like peaks coexist, and the valley between the two peaks is suppressed with the system size increasing. Thi...
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Percolation is perhaps the simplest example of a process exhibiting a phase transition and one of the most studied phenomena in statistical physics. The percolation transition is continuous if sites/bonds are occupied independently with the same probability. However, alternative rules for the occupation of sites/bonds might affect the order of the transition. A recent set of rules proposed by A...
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Percolation is one of the most studied processes in statistical physics. A recent paper by Achlioptas [Science 323, 1453 (2009)] showed that the percolation transition, which is usually continuous, becomes discontinuous ("explosive") if links are added to the system according to special cooperative rules (Achlioptas processes). In this paper, we present a detailed numerical analysis of Achliopt...
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ژورنال
عنوان ژورنال: Physical Review Letters
سال: 2010
ISSN: 0031-9007,1079-7114
DOI: 10.1103/physrevlett.105.255701