Speaker
Sergey Dorogovtsev
(University of Aveiro)
Description
We present the theory of explosive percolation. Recently
a discontinuous percolation transition was reported in a
new "explosive percolation" problem for irreversible systems
[D. Achlioptas, R. M. D'Souza, and J. Spencer, Science 323,
1453 (2009)] in striking contrast to ordinary percolation. We
show that the "explosive percolation" transition is actually a
continuous, second order phase transition though with a
uniquely small critical exponent of the percolation cluster size.
Thus there is no explosion at the "explosive percolation"
transition.
Using a wide class of representative models, we describe the
unusual scaling properties of this transition and find a set of its
scaling functions and critical exponents and dimensions. In
particular, we find that the upper critical dimensions for such
phase transitions are remarkably low.
[1] R. A. da Costa, S. N. Dorogovtsev, A. V. Goltsev, and J. F.
F. Mendes, arXiv:1009.2534.
[2] S. N. Dorogovtsev, Lectures on Complex Networks
(Oxford University Press, Oxford, 2010).
