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Explosive percolation transition is actually continuous
Authors:da Costa R A  Dorogovtsev S N  Goltsev A V  Mendes J F F
Institution:Departamento de Física da Universidade de Aveiro, I3N, 3810-193 Aveiro, Portugal.
Abstract: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 consider a representative model which shows 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. We describe the unusual scaling properties of this transition and find its critical exponents and dimensions.
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