Hybrid phase transition into an absorbing state: Percolation and avalanches

作者：Lee Deokjae; Choi S; Stippinger M; Kertesz J; Kahng B^*

来源：PHYSICAL REVIEW E, 2016, 93(4): 042109.

DOI：10.1103/PhysRevE.93.042109

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-Renyi 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 beta(m) of the order parameter is 1/2 under general conditions, while the value of the exponent gamma(m) 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, beta(a) and gamma(a). These two critical behaviors are coupled by a scaling law: 1 - beta(m) = gamma(a).

• 出版日期2016-4-8