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Chin. Phys. B, 2018, Vol. 27(10): 106402    DOI: 10.1088/1674-1056/27/10/106402
CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES Prev   Next  

Study on the phase transition of the fractal scale-free networks

Qing-Kuan Meng(孟庆宽), Dong-Tai Feng(冯东太), Yu-Ping Sun(孙玉萍), Ai-Ping Zhou(周爱萍), Yan Sun(孙艳), Shu-Gang Tan(谭树刚), Xu-Tuan Gao(高绪团)
School of Physics and Opto-Electronic Engineering, Shandong University of Technology, Zibo 255049, China
Abstract  

Based on the Ising spin, the phase transition on fractal scale-free networks with tree-like skeletons is studied, where the loops are generated by local links. The degree distribution of the tree-like skeleton satisfies the power-law form P(k)~k-δ. It is found that when δ ≥ 3, the renormalized scale-free network will have the same degree distribution as the original network. For a special case of δ=4.5, a ferromagnetic to paramagnetic transition is found and the critical temperature is determined by the box-covering renormalization method. By keeping the structure of the fractal scale-free network constant, the numerical relationship between the critical temperature and the network size is found, which is the form of power law.

Keywords:  fractal scale-free network      phase transition      renormalization  
Received:  14 March 2018      Revised:  11 July 2018      Accepted manuscript online: 
PACS:  64.60.al (Fractal and multifractal systems)  
  64.60.-i (General studies of phase transitions)  
  89.75.-k (Complex systems)  
Fund: 

Project supported by the Natural Science Foundation of Shandong Province, China (Grant No. ZR2014EL002).

Corresponding Authors:  Qing-Kuan Meng, Dong-Tai Feng     E-mail:  qkmeng@sdut.edu.cn;fengdongtai@sdut.edu.cn

Cite this article: 

Qing-Kuan Meng(孟庆宽), Dong-Tai Feng(冯东太), Yu-Ping Sun(孙玉萍), Ai-Ping Zhou(周爱萍), Yan Sun(孙艳), Shu-Gang Tan(谭树刚), Xu-Tuan Gao(高绪团) Study on the phase transition of the fractal scale-free networks 2018 Chin. Phys. B 27 106402

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