Percolation with Multiple Giant Clusters

Details Percolation with Multiple Giant Clusters Percolation with Multiple Giant Clusters

2005-01-10

arxiv.org/abs/cond-mat/0501218v1

J. Phys. A 38, L417 (2005)

Physics

Condensed Matter

Statistical Mechanics

4 pages, 3 figures

Scientific paper

10.1088/0305-4470/38/23/L01

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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