TY - JOUR

T1 - Hybrid phase transition into an absorbing state

T2 - Percolation and avalanches

AU - Lee, Deokjae

AU - Choi, S.

AU - Stippinger, M.

AU - Kertész, J.

AU - Kahng, B.

N1 - Publisher Copyright:
© 2016 American Physical Society.

PY - 2016/4/8

Y1 - 2016/4/8

N2 - 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 Erdos-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.

AB - 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 Erdos-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.

UR - http://www.scopus.com/inward/record.url?scp=84963517186&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.93.042109

DO - 10.1103/PhysRevE.93.042109

M3 - Article

AN - SCOPUS:84963517186

SN - 2470-0045

VL - 93

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

IS - 4

M1 - 042109

ER -