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Percolation with Multiple Giant Clusters

E. Ben-Naim·P. L. Krapivsky
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Abstract

We study the evolution of percolation with freezing. Specifically, we consider cluster formation via two competing processes: irreversible aggregation and freezing. We find that when the freezing rate exceeds a certain threshold, the percolation transition is suppressed. Below this threshold, the system undergoes a series of percolation transitions with multiple giant clusters ("gels") formed. Giant clusters are not self-averaging as their total number and their sizes fluctuate from realization to realization. The size distribution F_k, of frozen clusters of size k, has a universal tail, F_k ~ k^{-3}. We propose freezing as a practical mechanism for controlling the gel size.

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E. Ben-Naim, P. L. Krapivsky. 2005-01-10. Percolation with Multiple Giant Clusters. https://doi.org/10.1088/0305-4470%2F38%2F23%2Fl01

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