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Hybrid phase transition into an absorbing state: Percolation and avalanches

Deokjae Lee1, S. Choi1, M. Stippinger2, J. Kertész2,3, and B. Kahng1,*

  • 1CCSS, CTP and Department of Physics and Astronomy, Seoul National University, Seoul 08826, Korea
  • 2Department of Theoretical Physics, Budapest University of Technology and Economics, Budapest H-1111, Hungary
  • 3Center for Network Science, Central European University, Budapest H-1051, Hungary

  • *bkahng@snu.ac.kr
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Phys. Rev. E 93, 042109 – Published 8 April, 2016

DOI: https://doi.org/10.1103/PhysRevE.93.042109

Abstract

Interdependent networks are more fragile under random attacks than simplex networks, because interlayer dependencies lead to cascading failures and finally to a sudden collapse. This is a hybrid phase transition (HPT), meaning that at the transition point the order parameter has a jump but there are also critical phenomena related to it. Here we study these phenomena on the Erdős-Rényi and the two-dimensional interdependent networks and show that the hybrid percolation transition exhibits two kinds of critical behaviors: divergence of the fluctuations of the order parameter and power-law size distribution of finite avalanches at a transition point. At the transition point global or “infinite” avalanches occur, while the finite ones have a power law size distribution; thus the avalanche statistics also has the nature of a HPT. The exponent βm of the order parameter is 1/2 under general conditions, while the value of the exponent γm characterizing the fluctuations of the order parameter depends on the system. The critical behavior of the finite avalanches can be described by another set of exponents, βa and γa. These two critical behaviors are coupled by a scaling law: 1−βm=γa.

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Phys. Rev. E 93, 042109– Published 8 April, 2016
  • Received 22 December 2015

©2016 American Physical Society

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