Percolation on branching simplicial and cell complexes and its relation to interdependent percolation

Abstract

Network geometry has strong effects on network dynamics. In particular, the underlying hyperbolic geometry of discrete manifolds has recently been shown to affect their critical percolation properties. Here we investigate the properties of link percolation in non-amenable two-dimensional branching simplicial and cell complexes, i.e., simplicial and cell complexes in which the boundary scales like the volume. We establish the relation between the equations determining the percolation probability in random branching cell complexes and the equation for interdependent percolation in multiplex networks with inter-layer degree correlation equal to one. By using this relation we show that branching cell complexes can display more than two percolation phase transitions: the upper percolation transition, the lower percolation transition, and one or more intermediate phase transitions. At these additional transitions the percolation probability and the fractal exponent both feature a discontinuity. Furthermore, by using the renormalization group theory we show that the upper percolation transition can belong to various universality classes including the Berezinskii-Kosterlitz-Thouless (BKT) transition, the discontinuous percolation transition, and continuous transitions with anomalous singular behavior that generalize the BKT transition.

arXiv comment(16 pages, 10 figures)

References in corpus (38)

• Catastrophic cascade of failures in interdependent networks
• Multilayer Networks
• The structure and dynamics of multilayer networks
• Critical phenomena in complex networks
• Simplicial models of social contagion
• Interdependent networks: Reducing the coupling strength leads to a change from a first to second order percolation transition
• Pseudofractal Scale-free Web
• Avalanche Collapse of Interdependent Network
• Abrupt Desynchronization and Extensive Multistability in Globally Coupled Oscillator Simplices
• "Explosive Percolation" Transition is Actually Continuous
• Explosive Phenomena in Complex Networks
• Multiple percolation transitions in a configuration model of network of networks
• Emergent Hyperbolic Network Geometry
• Simplicial complexes and complex systems
• Inverted Berezinskii-Kosterlitz-Thouless Singularity and High-Temperature Algebraic Order in an Ising Model on a Scale-Free Hierarchical-Lattice Small-World Network
• Network geometry with flavor: from complexity to quantum geometry
• Recent advances and open challenges in percolation
• Interdisciplinary and physics challenges of Network Theory
• Ordinary Percolation with Discontinuous Transitions
• Recent advances of percolation theory in complex networks
• Phase Transitions on Nonamenable Graphs
• Synchronization in Network Geometries with Finite Spectral Dimension
• Rare events and discontinuous percolation transitions
• Topological Percolation on Hyperbolic Simplicial Complexes
• Small-World Bonds and Patchy Percolation on the Hanoi Network
• Network Geometry and Complexity
• How does bond percolation happen in coloured networks?
• Generating-function approach for bond percolations in hierarchical networks
• Renormalization group for evolving networks
• Transition-type change between an inverted Berezinskii-Kosterlitz-Thouless transition and an abrupt transition in the bond percolation on a random hierarchical small-world network
• Renormalization group for link percolation on planar hyperbolic manifolds
• Crossing on hyperbolic lattices
• Scaling of Clusters near Discontinuous Percolation Transitions in Hyperbolic Networks
• Classification of critical phenomena in hierarchical small-world networks
• Percolation Thresholds in Hyperbolic Lattices
• Enhancing the robustness of a multiplex network leads to multiple discontinuous percolation transitions
• From explosive to infinite-order transitions on a hyperbolic network
• Renormalization-group theory of the abnormal singularities at the critical-order transition in bond percolation on pointed hierarchical graphs

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• Growing scale-free simplices
• The dynamic nature of percolation on networks with triadic interactions
• The spectral dimension of simplicial complexes: a renormalization group theory
• The higher-order spectrum of simplicial complexes: a renormalization group approach
• Stochastic epidemic model on a simplicial complex
• Unveiling the Importance of Nonshortest Paths in Quantum Networks
• Random Simplicial Complexes: Models and Phenomena
• Impact of assortative mixing by mask-wearing on the propagation of epidemics in networks
• Renormalization group theory of percolation on pseudo-fractal simplicial and cell complexes
• Critical time-dependent branching process modelling epidemic spreading with containment measures
• Networks with degree-degree correlations is a special case of edge-coloured random graphs