"Explosive Percolation" Transition is Actually Continuous
arXiv:1009.2534 · doi:10.1103/PhysRevLett.105.255701
Abstract
The basic notion of percolation in physics assumes the emergence of a giant connected (percolation) cluster in a large disordered system when the density of connections exceeds some critical value. Until recently, the percolation phase transitions were believed to be continuous, however, in 2009, a remarkably different, discontinuous phase transition was reported in a new so-called "explosive percolation" problem. Each link in this problem is established by a specific optimization process. Here, employing strict analytical arguments and numerical calculations, we find that in fact the "explosive percolation" transition is continuous though with an uniquely small critical exponent of the percolation cluster size. These transitions provide a new class of critical phenomena in irreversible systems and processes.
arXiv comment22 pages, 4 figures, 1 table
References in corpus (10)
- Critical phenomena in complex networks
- k-core organization of complex networks
- Scaling Theory and Exactly Solved Models In the Kinetics of Irreversible Aggregation
- Explosive percolation in scale-free networks
- Explosive percolation via control of the largest cluster
- Percolation Transitions in Scale-Free Networks under Achlioptas Process
- Explosive percolation: a numerical analysis
- Local cluster aggregation models of explosive percolation
- Scaling behavior of explosive percolation on the square lattice
- Finite-size scaling theory for explosive percolation transitions
Cited by in corpus (155)
- Catastrophic cascade of failures in interdependent networks
- The Kuramoto model in complex networks
- The physics of higher-order interactions in complex systems
- Robustness and resilience of complex networks
- Recent advances in percolation theory and its applications
- Explosive transitions in complex networks' structure and dynamics: percolation and synchronization
- Percolation on complex networks: Theory and application
- Assortativity Decreases the Robustness of Interdependent Networks
- Self-organized adaptation of a simple neural circuit enables complex robot behaviour
- Impact of Single Links in Competitive Percolation -- How complex networks grow under competition
- Controllability transition and nonlocality in network control
- Explosive Phenomena in Complex Networks
- Explosive Percolation is Continuous, but with Unusual Finite Size Behavior
- Statistical physics approaches to the complex Earth system
- Explosive Percolation: Novel critical and supercritical phenomena
- Recent advances and open challenges in percolation
- Avoiding a Spanning Cluster in Percolation Models
- Core percolation on complex networks
- Articulation Points in Complex Networks
- k-Core percolation on multiplex networks
- Dynamical Systems on Networks: A Tutorial
- Strongly discontinuous explosive percolation with multiple giant components
- Ordinary Percolation with Discontinuous Transitions
- Discontinuous Percolation Transitions in Epidemic Processes, Surface Depinning in Random Media and Hamiltonian Random Graphs
- Are Percolation Transitions always Sharpened by Making Networks Interdependent?
- Tricritical point in explosive percolation
- Recent advances of percolation theory in complex networks
- Continuity of the Explosive Percolation Transition
- Achlioptas process phase transitions are continuous
- The dynamic nature of percolation on networks with triadic interactions
- Disorder induces explosive synchronization
- Percolation framework to describe El Niño conditions
- Tricritical point in heterogeneous k-core percolation
- Rare events and discontinuous percolation transitions
- Network Observability Transitions
- Explosive oscillation death in coupled Stuart-Landau oscillators
- Topological Percolation on Hyperbolic Simplicial Complexes
- Solution of the explosive percolation quest: Scaling functions and critical exponents
- Anomalous discontinuity at the percolation critical point of active gels
- Hyperedge overlap drives explosive collective behaviors in systems with higher-order interactions
- Critical noise of majority-vote model on complex networks
- Using explosive percolation in analysis of real-world networks
- Mixed order transition and condensation in exactly soluble one dimensional spin model
- Crackling Noise in Fractional Percolation -- Randomly distributed discontinuous jumps in explosive percolation
- Explosive site percolation and finite size hysteresis
- Gaussian model of explosive percolation in three and higher dimensions
- Suppression effect on explosive percolations
- Bohman-Frieze-Wormald model on the lattice, yielding a discontinuous percolation transition
- Achlioptas processes are not always self-averaging
- Explosive synchronization transitions in complex neural network
- Analysis of cluster explosive synchronization in complex networks
- Networks in Motion
- Connectivity disruption sparks explosive epidemic spreading
- Deriving an underlying mechanism for discontinuous percolation
- Solution of the explosive percolation quest. II. Infinite-order transition produced by the initial distributions of clusters
- Explosive site percolation with a product rule
- Transport on exploding percolation clusters
- Diverse types of percolation transitions
- Discontinuous percolation transitions in real physical systems
- Explosive Percolation: Unusual Transitions of a Simple Model
- Sensitivity of directed networks to the addition and pruning of edges and vertices
- Unstable supercritical discontinuous percolation transitions
- Percolation on branching simplicial and cell complexes and its relation to interdependent percolation
- Crossover phenomena of percolation transition in evolution networks with hybrid attachment
- Phase diagrams of interacting spreading dynamics in complex networks
- Network-complement transitions, symmetries, and cluster synchronization
- Continuous Percolation Phase Transitions of Two-dimensional Lattice Networks under a Generalized Achlioptas Process
- Correlated percolation and tricriticality
- Antagonistic Phenomena in Network Dynamics
- Criterion for explosive percolation transitions on complex networks
- Explosive Percolation Obeys Standard Finite-Size Scaling in an Event-based Ensemble
- Partial inertia induces additional phase transition in the explosive majority vote model
- Exploring the adaptive voter model dynamics with a mathematical triple jump
- Explosive percolations on the Bethe Lattice
- Renormalization group for link percolation on planar hyperbolic manifolds
- About the fastest growth of Order Parameter in Models of Percolation
- Changes in the gradient percolation transition caused by an Allee effect
- Critical exponents of the explosive percolation transition
- Weakly Explosive Percolation in Directed Networks
- Two Types of Discontinuous Percolation Transitions in Cluster Merging Processes
- Percolation on interdependent networks with a fraction of antagonistic interactions
- Scaling of Clusters near Discontinuous Percolation Transitions in Hyperbolic Networks
- Sensitive Dependence of Optimal Network Dynamics on Network Structure
- Non-Local Product Rules for Percolation
- Choice-Driven Phase Transition in Complex Networks
- Explosive percolation in graphs
- A percolation model with continuously varying exponents
- Agglomerative Percolation on Bipartite Networks: A Novel Type of Spontaneous Symmetry Breaking
- Percolation properties of growing networks under an Achlioptas process
- Controlling percolation with limited resources
- Transmission of packets on a hierarchical network: Statistics and explosive percolation
- Some Applications of the Percolation Theory. Brief Review of the Century Beginning
- Percolation model with an additional source of disorder
- Given enough choice, simple local rules percolate discontinuously
- Inverting the Achlioptas rule for explosive percolation
- Explosive percolation in thresholded networks
- From explosive to infinite-order transitions on a hyperbolic network
- Unified framework for hybrid percolation transitions based on microscopic dynamics
- Method for estimating critical exponents in percolation processes with low sampling
- Explosive percolation in finite dimensions
- The phase transition in bounded-size Achlioptas processes
- Explosive Ising
- Watersheds and Explosive percolation
- Product-Sum universality and Rushbrooke inequality in explosive percolation
- A minimal exactly solved model with the extreme Thouless effect
- Information entropy of classical versus explosive percolation
- Theory of deflagration in disordered media
- Alternative criterion for two-dimensional wrapping percolation
- Criticality and Continuity of Explosive Site Percolation in Random Networks
- Percolation under Noise: Detecting Explosive Percolation Using the Second Largest Component
- Reversible first-order transition in Pauli percolation
- Popularity-Driven Networking
- Analysis on the evolution process of BFW-like model with explosive percolation of multiple giant components
- Scaling relations and finite-size scaling in gravitationally correlated lattice percolation models
- Explosive percolation on scale-free multifractal weighted planar stochastic lattice
- History-dependent percolation in two dimensions
- Discontinuous percolation in diffusion-limited cluster aggregation
- Degree product rule tempers explosive percolation in the absence of global information
- Explosive Percolation on Directed Networks Due to Monotonic Flow of Activity
- Mixed-order phase transition in a minimal, diffusion based spin model
- Spectral Anlysis on Explosive Percolation
- Emergence of biconnected clusters in explosive percolation
- Degree-dependent network growth: From preferential attachment to explosive percolation
- Scaling behavior of information entropy in explosive percolation transitions
- Coagulation with product kernel and arbitrary initial conditions: Exact kinetics within the Marcus-Lushnikov framework
- Adhesion-induced Discontinuous Transitions and Classifying Social Networks
- Convergence of Achlioptas processes via differential equations with unique solutions
- A hybrid percolation transition at a finite transition point in scale-free networks
- Opinion formation models on a gradient
- Structural Properties of Networks Grown via an Achlioptas Process
- Universality class of explosive percolation in Barabási-Albert networks
- Explosive rigidity percolation in kirigami
- Link rewiring with local information--induced hybrid percolation transitions
- Percolation Transitions in Growing Networks Under Achlioptas Processes: Analytic Solutions
- Crossover behavior of conductivity in a discontinuous percolation model
- Explosive percolation on the Bethe lattice is ordinary
- Coalescense with arbitrary-parameter kernels and monodisperse initial conditions: A study within combinatorial framework
- Coherent transport over an explosive percolation lattice
- Emergence of strongly connected giant components in continuum disk-spin percolation
- Induced Percolation on Networked Systems
- A Novel Approach to Discontinuous Bond Percolation Transition
- Discontinuous percolation via suppression of neighboring clusters in a network
- Network-Growth Rule Dependence of Fractal Dimension of Percolation Cluster on Square Lattice
- Complex networks of interacting stochastic tipping elements: cooperativity of phase separation in the large-system limit
- Random growth lattice filling model of percolation: a crossover from continuous to discontinuous transition
- Discontinuous transition in explosive percolation via local suppression
- Thermodynamic analysis of diverse percolation transitions
- Percolation critical exponents in cluster kinetics of pulse-coupled oscillators
- Evolution of autocatalytic sets in a competitive percolation model
- Entanglement percolation enhanced by the power of choice
- Phase transition in the diffusion and bootstrap percolation models on regular random and Erdős-Rényi networks
- Discontinuous emergence of a giant cluster in assortative scale-free networks
- Explosive rigidity percolation in origami
- Shortest-path percolation on scale-free networks
- Kinetics of Aggregation with Choice