Hybrid Percolation Transition in Cluster Merging Processes: Continuously Varying Exponents

作者：Cho Y S^*; Lee J S; Herrmann H J; Kahng B

来源：Physical Review Letters, 2016, 116(2): 025701.

DOI：10.1103/PhysRevLett.116.025701

Consider growing a network, in which every new connection is made between two disconnected nodes. At least one node is chosen randomly from a subset consisting of g fraction of the entire population in the smallest clusters. Here we show that this simple strategy for improving connection exhibits a more unusual phase transition, namely a hybrid percolation transition exhibiting the properties of both first-order and second-order phase transitions. The cluster size distribution of finite clusters at a transition point exhibits power-law behavior with a continuously varying exponent tau in the range 2 < tau (g) <= 2.5. This pattern reveals a necessary condition for a hybrid transition in cluster aggregation processes, which is comparable to the power-law behavior of the avalanche size distribution arising in models with link-deleting processes in interdependent networks.

• 出版日期2016-1-15