title: Explosive percolation on the Bethe lattice.
abstract: Based on self-consistent equations of the order parameter P∞ and the mean cluster size S, we develop a self-consistent simulation method for arbitrary percolation on the Bethe lattice (infinite homogeneous Cayley tree). By applying the self-consistent simulation to well-known percolation models, random bond percolation, and bootstrap percolation, we obtain prototype functions for continuous and discontinuous phase transitions. By comparing key functions obtained from self-consistent simulations for Achlioptas models with a product rule and a sum rule to the prototype functions, we show that the percolation transition of Achlioptas models on the Bethe lattice is continuous regardless of details of growth rules.
authors.affiliation: Department of Physics and Research Institute for Basic Sciences, Kyung Hee University, Seoul 130-701, Korea.
authors.forename: Huiseung
authors.initials: H
authors.lastname: Chae
authors.forename: Soon-Hyung
authors.initials: SH
authors.lastname: Yook
authors.forename: Yup
authors.initials: Y
authors.lastname: Kim