Characteristics of the Explosive Percolation Transition

  • R. A. da Costa
  • S. N. Dorogovtsev
  • A. V. Goltsev
  • J. F. F. Mendes
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 57)

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.

Keywords

Explosive 

Notes

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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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • R. A. da Costa
    • 1
  • S. N. Dorogovtsev
    • 1
    • 2
  • A. V. Goltsev
    • 1
    • 2
  • J. F. F. Mendes
    • 1
  1. 1.Department of Physics and I3NUniversity of Aveiro, Campus Universitário de SantiagoAveiroPortugal
  2. 2.A.F. Ioffe Physico-Technical InstituteSt. PetersburgRussia

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