Abstract
An unusual phase transition was recently discovered in a bunch of evolving network models in which each new connection between nodes is selected from several possibilities by an optimization algorithm. First studies (simulations) of these systems interpreted the emergence of a percolation cluster (giant connected component) as a discontinuous phase transition, and so the transition was said to be “explosive.” We have shown, however, that this transition is actually continuous but with uniquely small critical exponent of the percolation cluster size. Here we propose an efficient method for finding the characteristics of this second-order transition for a set of explosive percolation models. For each of the models, with high precision, we obtain critical exponents and amplitudes, and the critical point.
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Acknowledgements
This work was partially supported by the FCT projects PTDC: FIS/71551/2006, FIS/108476/2008, SAU-NEU/103904/2008, MAT/114515/2009, and PEst-C/CTM/LA0025/2011.
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da Costa, R.A., Dorogovtsev, S.N., Goltsev, A.V., Mendes, J.F.F. (2014). Characteristics of the Explosive Percolation Transition. In: Grácio, C., Fournier-Prunaret, D., Ueta, T., Nishio, Y. (eds) Nonlinear Maps and their Applications. Springer Proceedings in Mathematics & Statistics, vol 57. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9161-3_3
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DOI: https://doi.org/10.1007/978-1-4614-9161-3_3
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