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Abstract: We introduce a cluster growth process that provides a clear connectionbetween equilibrium statistical mechanics and an explosive percolation modelsimilar to the one recently proposed by Achlioptas et al. Science 323, 14532009. We show that the following two ingredients are essential for obtainingan abrupt first-order transition in the fraction of the system occupied bythe largest cluster: i the size of all growing clusters should be keptapproximately the same, and ii the inclusion of merging bonds i.e., bondsconnecting vertices in different clusters should dominate with respect to theredundant bonds i.e., bonds connecting vertices in the same cluster.Moreover, in the extreme limit where only merging bonds are present, a completeenumeration scheme based on tree-like graphs can be used to obtain an exactsolution of our model that displays a first-order transition. Finally, theproposed mechanism can be viewed as a generalization of standard percolationthat discloses an entirely new family of models with potential application ingrowth and fragmentation processes of real network systems.



Author: A. A. Moreira, E. A. Oliveira, S. D. S. Reis, H. J. Herrmann, J. S. Andrade Jr

Source: https://arxiv.org/



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