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Chin. Phys. B, 2014, Vol. 23(7): 076401    DOI: 10.1088/1674-1056/23/7/076401

Characteristics of phase transitions via intervention in random networks

Jia Xiao (贾啸)a, Hong Jin-Song (洪劲松)a, Yang Hong-Chun (杨宏春)a, Yang Chun (杨春)b, Shi Xiao-Hong (史晓红)b, Hu Jian-Quan (胡建全)a
a School of Physical Electronics, University of Electronic Science and Technology of China, Chengdu 610054, China;
b School of Mathematical Science, University of Electronic Science and Technology of China, Chengdu 610054, China
Abstract  We present a percolation process in which the classical Erdös-Rényi (ER) random evolutionary network is intervened by the product rule (PR) from some moment t0. The parameter t0 is continuously tunable over the real interval [0, 1]. This model becomes the random network under the Achlioptas process at t0= 0 and the ER network at t0= 1. For the percolation process at t0≤ 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 t0 ≤ 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 t0. 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 t0> 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 t0< 1 and the ER network about different t0. The presented mechanism can be viewed as a two-stage percolation process that has many potential applications in the growth processes of real networks.
Keywords:  percolation      phase transitions      networks  
Received:  14 November 2013      Revised:  20 February 2014      Accepted manuscript online: 
PACS:  64.60.ah (Percolation)  
  64.60.-i (General studies of phase transitions) (Networks)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 61172115 and 60872029), the High Technology Research and Development Program of China (Grant No. 2008AA01Z206), the Aeronautics Foundation of China (Grant No. 20100180003), the Fundamental Research Funds for the Central Universities, China (Grant No. ZYGX2009J037), and Project 9140A07030513DZ02098, China.
Corresponding Authors:  Jia Xiao     E-mail:
About author:  64.60.ah; 64.60.-i;

Cite this article: 

Jia Xiao (贾啸), Hong Jin-Song (洪劲松), Yang Hong-Chun (杨宏春), Yang Chun (杨春), Shi Xiao-Hong (史晓红), Hu Jian-Quan (胡建全) Characteristics of phase transitions via intervention in random networks 2014 Chin. Phys. B 23 076401

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