Percolation with Multiple Giant Clusters
E. Ben-Naim and P.L. Krapivsky
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, $F_k\sim
k^{-3}$. We propose freezing as a practical mechanism for controlling
the gel size.
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