Explosive percolation in networks

 

FILIPPO RADICCHI

INSTITUTE FOR SCIENTIFIC INTERCHANGE FOUNDATION

 

Percolation is one of the most studied processes in statistical physics. Independently of the system, percolation is characterized by a continuous phase transition. If the standard rules of percolation are slightly modified and links are added to the system according to special cooperative rules, percolation changes its features and the transition becomes discontinuous or "explosive". This applies to many topologies ranging from d-dimensional lattices to regular networks. A particular case is offered by scale-free networks for which the transition is still continuous for values of the degree exponent smaller than three, while becomes again discontinuous for larger values. In any case, the cooperative process at the basis of explosive percolation produces an hybrid transition: the jump of the order parameter is typical of first-order transitions, but traces of analytical behavior, like power law distributions of cluster sizes, are still present.