We introduce a cluster growth process that provides a clear connection
between equilibrium statistical mechanics and an explosive percolation model
similar to the one recently proposed by Achlioptas et al. [Science 323, 1453
(2009)]. We show that the following two ingredients are essential for obtaining
an abrupt (first-order) transition in the fraction of the system occupied by
the largest cluster: (i) the size of all growing clusters should be kept
approximately the same, and (ii) the inclusion of merging bonds (i.e., bonds
connecting vertices in different clusters) should dominate with respect to the
redundant bonds (i.e., bonds connecting vertices in the same cluster).
Moreover, in the extreme limit where only merging bonds are present, a complete
enumeration scheme based on tree-like graphs can be used to obtain an exact
solution of our model that displays a first-order transition. Finally, the
proposed mechanism can be viewed as a generalization of standard percolation
that discloses an entirely new family of models with potential application in
growth and fragmentation processes of real network systems.Comment: 4 pages, 4 figure
