Explosive percolations on the Bethe Lattice

Abstract

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.

4 pages, 4 figures

References in corpus (8)

• "Explosive Percolation" Transition is Actually Continuous
• Explosive Percolation is Continuous, but with Unusual Finite Size Behavior
• Explosive percolation in scale-free networks
• Continuity of the Explosive Percolation Transition
• Finite-size scaling theory for explosive percolation transitions
• Suppression effect on explosive percolations
• Explosive site percolation with a product rule
• Explosive percolation in graphs

Cited by in corpus (11)

• Explosive transitions in complex networks' structure and dynamics: percolation and synchronization
• Explosive Percolation: Unusual Transitions of a Simple Model
• Unstable supercritical discontinuous percolation transitions
• Growth models on the Bethe lattice
• Spectral Anlysis on Explosive Percolation
• Scaling behavior of information entropy in explosive percolation transitions
• Link rewiring with local information--induced hybrid percolation transitions
• Explosive percolation on the Bethe lattice is ordinary
• Network-Growth Rule Dependence of Fractal Dimension of Percolation Cluster on Square Lattice
• Numerical Integration of the KPZ and Related Equations on Networks: The Case of the Cayley Tree
• Discontinuous emergence of a giant cluster in assortative scale-free networks