Exotic Critical Behavior of Weak Multiplex Percolation
| Autor: | José F. F. Mendes, Sergey N. Dorogovtsev, R. A. da Costa, G. J. Baxter |
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| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Connected component
Quadratic growth Physics Statistical Mechanics (cond-mat.stat-mech) Interdependent networks FOS: Physical sciences Disordered Systems and Neural Networks (cond-mat.dis-nn) Condensed Matter - Disordered Systems and Neural Networks 01 natural sciences Giant component Nonlinear Sciences - Adaptation and Self-Organizing Systems 010305 fluids & plasmas Discontinuity (geotechnical engineering) 0103 physical sciences Exponent Continuous phase transition Multiplex Statistical physics 010306 general physics Adaptation and Self-Organizing Systems (nlin.AO) Condensed Matter - Statistical Mechanics |
| Popis: | We describe the critical behavior of weak multiplex percolation, a generalization of percolation to multiplex or interdependent networks. A node can determine its active or inactive status simply by referencing neighboring nodes. This is not the case for the more commonly studied generalization of percolation to multiplex networks, the mutually connected clusters, which requires an interconnecting path within each layer between any two vertices in the giant mutually connected component. We study the emergence of a giant connected component of active nodes under the weak percolation rule, finding several non-typical phenomena. In two layers, the giant component emerges with a continuos phase transition, but with quadratic growth above the critical threshold. In three or more layers, a discontinuous hybrid transition occurs, similar to that found in the giant mutually connected component. In networks with asymptotically powerlaw degree distributions, defined by the decay exponent $\gamma$, the discontinuity vanishes but at $\gamma=1.5$ in three layers, more generally at $\gamma = 1+ 1/(M-1)$ in $M$ layers. Comment: 11 pages, 6 figures |
| Databáze: | OpenAIRE |
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