Percolation with Multiple Giant Clusters

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.

4 pages, 3 figures

References in corpus (4)

• Scaling Theory and Exactly Solved Models In the Kinetics of Irreversible Aggregation
• The Scaling Window of the 2-SAT Transition
• Unicyclic Components in Random Graphs
• Stochastic Aggregation: Rate Equations Approach

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• Genuine Non-Self-Averaging and Ultra-Slow Convergence in Gelation
• Jamming and Tiling in Aggregation of Rectangles
• Universality in boundary domain growth by sudden bridging
• Percolation with constant freezing