Exotic critical behavior of weak multiplex percolation

G. J. Baxter, R. A. da Costa, S. N. Dorogovtsev, and J. F. F. Mendes
Phys. Rev. E 102, 032301 – Published 1 September 2020

Abstract

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 nontypical phenomena. In two layers, the giant component emerges with a continuous 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 γ, the discontinuity vanishes but at γ=1.5 in three layers, more generally at γ=1+1/(M1) in M layers.

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  • Received 2 June 2020
  • Accepted 18 August 2020

DOI:https://doi.org/10.1103/PhysRevE.102.032301

©2020 American Physical Society

Physics Subject Headings (PhySH)

Interdisciplinary PhysicsNetworksStatistical Physics & Thermodynamics

Authors & Affiliations

G. J. Baxter, R. A. da Costa, S. N. Dorogovtsev, and J. F. F. Mendes

  • Department of Physics, University of Aveiro & I3N, Campus Universitário de Santiago, 3810-193 Aveiro, Portugal

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Issue

Vol. 102, Iss. 3 — September 2020

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