title: Hybrid Percolation Transition in Cluster Merging Processes: Continuously Varying Exponents.
abstract: 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 τ in the range 2<τ(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.
authors.affiliation: CCSS, CTP and Department of Physics and Astronomy, Seoul National University, Seoul 08826, Korea.
authors.forename: Y S
authors.initials: YS
authors.lastname: Cho
authors.affiliation: School of Physics, Korea Institute for Advanced Study, Seoul 02455, Korea.
authors.forename: J S
authors.initials: JS
authors.lastname: Lee
authors.affiliation: Computational Physics for Engineering Materials, Institute for Building Materials, ETH Zürich, 8093 Zürich, Switzerland.
authors.forename: H J
authors.initials: HJ
authors.lastname: Herrmann
authors.affiliation: CCSS, CTP and Department of Physics and Astronomy, Seoul National University, Seoul 08826, Korea.
authors.forename: B
authors.initials: B
authors.lastname: Kahng