Characteristics of phase transitions via intervention in random networks  

作　　者：贾啸 洪劲松 杨宏春 杨春 史晓红 胡建全 

机构地区：[1]School of Physical Electronics,University of Electronic Science and Technology of China [2]School of Mathematical Science,University of Electronic Science and Technology of China

出　　处：《Chinese Physics B》2014年第7期596-600,共5页中国物理B（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.61172115 and 60872029);the High Technology Research and DevelopmentProgram of China(Grant No.2008AA01Z206);the Aeronautics Foundation of China(Grant No.20100180003);the Fundamental Research Funds for theCentral Universities,China(Grant No.ZYGX2009J037);Project 9140A07030513DZ02098,China

摘　　要：We present a percolation process in which the classical Erdts-Rtnyi （ER） random evolutionary network is intervened by the product rule （PR） from some moment to. The parameter to is continuously tunable over the real interval [0, 1]. This model becomes the random network under the Achlioptas process at to = 0 and the ER network at to = 1. For the percolation process at to≤1, we introduce a relatively slow-growing point, after which the largest cluster begins growing faster than that in the ER model. A weakly discontinuous transition is generated in the percolation process at to ≤ 0.5. We take the relatively slow-growing point as the lower pseudotransition point and the maximum gap point of the order parameter as the upper pseudotransition point. The critical point can be approximately predicted by each fitting function of the two points about to. This contributes to understanding the rapid mergence of the large clusters at the critical point. The numerical simulations indicate that the lower pseudotransition point and the upper pseudotransition point are equal in the thermodynamic limit. When to 〉 0.5, the percolation processes generate a continuous transition. The scaling analyses of several quantities are presented, including the relatively slow-growing point, the duration of the relatively slow-growing process, as well as the relatively maximum strength between the percolation percolation at to 〈 1 and the ER network about different to. The presented mechanism can be viewed as a two-stage percolation process that has many potential applications in the growth processes of real networks.We present a percolation process in which the classical Erdts-Rtnyi （ER） random evolutionary network is intervened by the product rule （PR） from some moment to. The parameter to is continuously tunable over the real interval [0, 1]. This model becomes the random network under the Achlioptas process at to = 0 and the ER network at to = 1. For the percolation process at to≤1, we introduce a relatively slow-growing point, after which the largest cluster begins growing faster than that in the ER model. A weakly discontinuous transition is generated in the percolation process at to ≤ 0.5. We take the relatively slow-growing point as the lower pseudotransition point and the maximum gap point of the order parameter as the upper pseudotransition point. The critical point can be approximately predicted by each fitting function of the two points about to. This contributes to understanding the rapid mergence of the large clusters at the critical point. The numerical simulations indicate that the lower pseudotransition point and the upper pseudotransition point are equal in the thermodynamic limit. When to 〉 0.5, the percolation processes generate a continuous transition. The scaling analyses of several quantities are presented, including the relatively slow-growing point, the duration of the relatively slow-growing process, as well as the relatively maximum strength between the percolation percolation at to 〈 1 and the ER network about different to. The presented mechanism can be viewed as a two-stage percolation process that has many potential applications in the growth processes of real networks.

关 键 词：PERCOLATION phase transitions NETWORKS 

分 类 号：O357.3[理学—流体力学]