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.

15 pages, 5 figures

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Cited by in corpus (9)

• Explosive transitions in complex networks' structure and dynamics: percolation and synchronization
• Percolation on complex networks: Theory and application
• 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
• Inverting the Achlioptas rule for explosive percolation
• Critical phenomena of a hybrid phase transition in cluster merging dynamics
• On multi-scale percolation behaviour of the effective conductivity for the lattice model
• A hybrid percolation transition at a finite transition point in scale-free networks
• Kinetics of Aggregation with Choice