Explosive Percolation: Unusual Transitions of a Simple Model
arXiv:1405.0388 · doi:10.1016/j.physa.2014.03.085
Abstract
In this paper we review the recent advances on explosive percolation, a very sharp phase transition first observed by Achlioptas et al. (Science, 2009). There a simple model was proposed, which changed slightly the classical percolation process so that the emergence of the spanning cluster is delayed. This slight modification turns out to have a great impact on the percolation phase transition. The resulting transition is so sharp that it was termed explosive, and it was at first considered to be discontinuous. This surprising fact stimulated considerable interest in "Achlioptas processes". Later work, however, showed that the transition is continuous (at least for Achlioptas processes on Erdos networks), but with very unusual finite size scaling. We present a review of the field, indicate open "problems" and propose directions for future research.
arXiv comment27 pages, 4 figures, Review paper
References in corpus (48)
- Catastrophic cascade of failures in interdependent networks
- Interdependent networks: Reducing the coupling strength leads to a change from a first to second order percolation transition
- Explosive Synchronization Transitions in Scale-free Networks
- The critical effect of dependency groups on the function of networks
- "Explosive Percolation" Transition is Actually Continuous
- Impact of Single Links in Competitive Percolation -- How complex networks grow under competition
- Self-organized adaptation of a simple neural circuit enables complex robot behaviour
- Explosive Percolation is Continuous, but with Unusual Finite Size Behavior
- Explosive percolation in scale-free networks
- Explosive percolation via control of the largest cluster
- Percolation Transitions in Scale-Free Networks under Achlioptas Process
- Construction and Analysis of Random Networks with Explosive Percolation
- Explosive percolation: a numerical analysis
- Local cluster aggregation models of explosive percolation
- Avoiding a Spanning Cluster in Percolation Models
- Strongly discontinuous explosive percolation with multiple giant components
- Scaling behavior of explosive percolation on the square lattice
- Ordinary Percolation with Discontinuous Transitions
- Tricritical point in explosive percolation
- A new route to Explosive Percolation
- Continuity of the Explosive Percolation Transition
- Explosive Percolation in the Human Protein Homology Network
- A Hamiltonian approach for explosive percolation
- Percolation with long-range correlated disorder
- Finite-size scaling theory for explosive percolation transitions
- Using explosive percolation in analysis of real-world networks
- Fracturing ranked surfaces
- Explosive site percolation and finite size hysteresis
- Suppression effect on explosive percolations
- Gaussian model of explosive percolation in three and higher dimensions
- Bohman-Frieze-Wormald model on the lattice, yielding a discontinuous percolation transition
- Deriving an underlying mechanism for discontinuous percolation
- Explosive site percolation with a product rule
- Transport on exploding percolation clusters
- Discontinuous percolation transitions in real physical systems
- Unstable supercritical discontinuous percolation transitions
- Continuous Percolation Phase Transitions of Two-dimensional Lattice Networks under a Generalized Achlioptas Process
- Correlated percolation and tricriticality
- Explosive percolations on the Bethe Lattice
- About the fastest growth of Order Parameter in Models of Percolation
- Weakly Explosive Percolation in Directed Networks
- Percolation properties of growing networks under an Achlioptas process
- Transmission of packets on a hierarchical network: Statistics and explosive percolation
- Explosive Ising
- Criticality and Continuity of Explosive Site Percolation in Random Networks
- Generalized Achlioptas process for the delay of criticality in the percolation process
- Spectral Anlysis on Explosive Percolation
- Degree-dependent network growth: From preferential attachment to explosive percolation
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- Recent advances in percolation theory and its applications
- Explosive transitions in complex networks' structure and dynamics: percolation and synchronization
- Explosive Phenomena in Complex Networks
- Explosive Percolation: Novel critical and supercritical phenomena
- Additional complex conjugate feedback induced explosive death and multistabilities
- Potts Model with Invisible States: A Review
- From explosive to infinite-order transitions on a hyperbolic network
- Method for estimating critical exponents in percolation processes with low sampling
- Inverting the Achlioptas rule for explosive percolation
- Marginal dimensions of the Potts model with invisible states
- Product-Sum universality and Rushbrooke inequality in explosive percolation
- Explosive percolation on scale-free multifractal weighted planar stochastic lattice
- Degree product rule tempers explosive percolation in the absence of global information
- Hysteresis and criticality in hybrid percolation transitions
- Universality class of explosive percolation in Barabási-Albert networks
- Random growth lattice filling model of percolation: a crossover from continuous to discontinuous transition