Explosive Percolation
By: Nuno Araújo
From: ETH, Switzerland
At: Instituto de Investigação Interdisciplinar, Anfiteatro
[2011-01-27]
Percolation is one of the most often applied models in Statistical Physics. Based on random connectivity, this model is characterized by a second-order transition, at the percolation threshold, between a percolative and a nonpercolative state. The recent work by Achlioptas, D'Souza, and Spence open up the possibility of obtaining a first-order (explosive) percolation transition by changing the stochastic rule of bonds occupation. Despite the active research in this subject, several questions still open about the leading mechanism and the properties of the system. In our work we shed some light on how to obtain a first-order transition by showing that is solely necessary to control the size of the largest cluster, demoting the growth of a cluster differing significantly, in size, from the average one. As expected for a first-order transition, with the disclosed stochastic rule, a Gaussian cluster-size distribution and compact clusters are obtained. We also introduce an hybrid model with an additional external parameter, which interpolates between classical and explosive percolation. A tricritical point is identified and the tricritical crossover scaling analyzed.
N. A. M. Araújo and H. J. Herrmann, Explosive Percolation via Control of the Largest Cluster, Phys. Rev. Lett. 105, 035701 (2010).