Percolation with multiple giant clusters

We study mean-field 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 similar to k(-3). We propose freezing as a practical mechanism for controlling the gel size.