Solution of the explosive percolation quest: Scaling functions and critical exponents

Abstract

Percolation refers to the emergence of a giant connected cluster in a disordered system when the number of connections between nodes exceeds a critical value. The percolation phase transitions were believed to be continuous until recently when in a new so-called "explosive percolation" problem for a competition driven process, a discontinuous phase transition was reported. The analysis of evolution equations for this process showed however that this transition is actually continuous though with surprisingly tiny critical exponents. For a wide class of representative models, we develop a strict scaling theory of this exotic transition which provides the full set of scaling functions and critical exponents. This theory indicates the relevant order parameter and susceptibility for the problem, and explains the continuous nature of this transition and its unusual properties.

arXiv comment15 pages, 5 figures

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• Explosive transitions in complex networks' structure and dynamics: percolation and synchronization
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• Explosive Phenomena in Complex Networks
• Explosive Percolation: Novel critical and supercritical phenomena
• Hybrid Percolation Transition in Cluster Merging Processes: Continuously Varying Exponents
• Anomalous discontinuity at the percolation critical point of active gels
• Solution of the explosive percolation quest. II. Infinite-order transition produced by the initial distributions of clusters
• Sensitivity of directed networks to the addition and pruning of edges and vertices
• Scaling of percolation transitions on Erdös-Rényi networks under centrality-based attacks
• Inverting the Achlioptas rule for explosive percolation
• Critical phenomena of a hybrid phase transition in cluster merging dynamics
• Information entropy of classical versus explosive percolation
• On multi-scale percolation behaviour of the effective conductivity for the lattice model
• Explosive percolation on scale-free multifractal weighted planar stochastic lattice
• Scaling behavior of information entropy in explosive percolation transitions
• Percolation Transitions in Growing Networks Under Achlioptas Processes: Analytic Solutions
• A hybrid percolation transition at a finite transition point in scale-free networks
• Link rewiring with local information--induced hybrid percolation transitions
• Explosive percolation on the Bethe lattice is ordinary
• Thermodynamic analysis of diverse percolation transitions
• Discontinuous percolation via suppression of neighboring clusters in a network
• Kinetics of Aggregation with Choice
• Discontinuous emergence of a giant cluster in assortative scale-free networks