Percolation with Multiple Giant Clusters

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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 Fₖ, of frozen clusters of size k, has a universal tail, Fₖ k⁻³. We propose freezing as a practical mechanism for controlling the gel size.