Explosive percolations on the Bethe Lattice

Details Explosive percolations on the Bethe Lattice Explosive percolations on the Bethe Lattice

2012-01-20

arxiv.org/abs/1201.4218v1

Physics

Condensed Matter

Statistical Mechanics

4 pages, 4 figures

Scientific paper

Based on the self-consistent equations of the order parameter $P_\infty$ and the mean cluster size $S$, we develop a novel self-consistent simulation (SCS) method for arbitrary percolation on the Bethe lattice (infinite homogeneous Cayley tree). By applying SCS to the well-known percolation models, random bond percolation and bootstrap percolation, we obtain prototype functions for continuous and discontinuous phase transitions. By comparing the key functions obtained from SCSs for the Achlioptas processes (APs) with a product rule and a sum rule to the prototype functions, we show that the percolation transition of AP models on the Bethe lattice is continuous regardless of details of growth rules.

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