Explosive percolation: A numerical analysis
Radicchi, F, Fortunato, SPhys. Rev. E 81, 036110 (2010)
Times cited: 61
Abstract
Percolation is one of the most studied processes in statistical
physics. A recent paper by Achlioptas et al. [Science 323, 1453
(2009)]
showed that the percolation transition, which is usually continuous,
becomes discontinuous (“explosive”) if links are added to the system
according to special cooperative rules (Achlioptas processes). In this
paper, we present a detailed numerical analysis of Achlioptas processes
with product rule on various systems, including lattices, random
networks a la Erdos-Renyi, and scale-free networks. In all cases, we
recover the explosive transition by Achlioptas et al. However, the
explosive percolation transition is kind of hybrid as, despite the
discontinuity of the order parameter at the threshold, one observes
traces of analytical behavior such as power-law distributions of
cluster sizes. In particular, for scale-free networks with degree
exponent lambda < 3, all relevant percolation variables display
power-law scaling, just as in continuous second-order phase
transitions.