Unified framework for hybrid percolation transitions based on microscopic dynamics
arXiv:2307.03584 · doi:10.1016/j.chaos.2024.114981
Abstract
A hybrid percolation transition (HPT) exhibits both discontinuity of the order parameter and critical behavior at the transition point. Such dynamic transitions can occur in two ways: by cluster pruning with suppression of loop formation of cut links or by cluster merging with suppression of the creation of large clusters. While the microscopic mechanism of the former is understood in detail, a similar framework is missing for the latter. By studying two distinct cluster merging models, we uncover the universal mechanism of the features of HPT-s at a microscopic level. We find that these features occur in three steps: (i) medium-sized clusters accumulate due to the suppression rule hindering the growth of large clusters, (ii) those medium size clusters eventually merge and a giant cluster increases rapidly, and (iii) the suppression effect becomes obsolete and the kinetics is governed by the Erdős-Rényi type of dynamics. We show that during the second and third period, the growth of the largest component must proceed in the form of a Devil's staircase. We characterize the critical behavior by two sets of exponents associated with the order parameter and cluster size distribution, which are related to each other by a scaling relation. Extensive numerical simulations are carried out to support the theory where a specific method is applied for finite-size scaling analysis to enable handling the large fluctuations of the transition point. Our results provide a unified theoretical framework for the HPT.
arXiv comment15 pages, 14 figures, 4 tables
References in corpus (37)
- Catastrophic cascade of failures in interdependent networks
- Critical phenomena in complex networks
- k-core organization of complex networks
- Explosive Synchronization Transitions in Scale-free Networks
- Avalanche Collapse of Interdependent Network
- "Explosive Percolation" Transition is Actually Continuous
- Why is the DNA Denaturation Transition First Order?
- Percolation Theory on Interdependent Networks Based on Epidemic Spreading
- Thermodynamic limit of the first-order phase transition in the Kuramoto model
- Bootstrap Percolation on Complex Networks
- Explosive Percolation: Novel critical and supercritical phenomena
- Recent advances and open challenges in percolation
- Construction and Analysis of Random Networks with Explosive Percolation
- Kuramoto model with frequency-degree correlations on complex networks
- Jamming Percolation and Glass Transitions in Lattice Models
- Avoiding a Spanning Cluster in Percolation Models
- Strongly discontinuous explosive percolation with multiple giant components
- Cluster aggregation model for discontinuous percolation transition
- Heterogeneous-k-core versus Bootstrap Percolation on Complex Networks
- Weak percolation on multiplex networks
- Recent advances of percolation theory in complex networks
- Kinetic Theory of Random Graphs: from Paths to Cycles
- Hybrid Phase Transition into an Absorbing State: Percolation and Avalanches
- Hybrid Percolation Transition in Cluster Merging Processes: Continuously Varying Exponents
- Critical dynamics of the k-core pruning process
- Interevent time distribution, burst, and hybrid percolation transition
- First-order phase transitions in outbreaks of co-infectious diseases and the extended general epidemic process
- Diverse types of percolation transitions
- Critical behavior of -core percolation: Numerical studies
- Origin of the mixed-order transition in multiplex networks: the Ashkin-Teller model
- Mixed-order phase transition in a colloidal crystal
- Mixed-order phase transition in a two-step contagion model with single infectious seed
- Critical behavior of a two-step contagion model with multiple seeds
- Critical phenomena of a hybrid phase transition in cluster merging dynamics
- Sudden spreading of infections in an epidemic model with a finite seed fraction
- Hysteresis and criticality in hybrid percolation transitions
- A hybrid percolation transition at a finite transition point in scale-free networks