Continuity of the Explosive Percolation Transition

Details Continuity of the Explosive Percolation Transition Continuity of the Explosive Percolation Transition

2011-03-23

arxiv.org/abs/1103.4439v3

Physics

Condensed Matter

Statistical Mechanics

Some corrections during the review

Scientific paper

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 $N\rightarrow\infty$. 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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