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

doi:10.1088/1674-1056/27/10/106402

中国物理B ›› 2018, Vol. 27 ›› Issue (10): 106402-106402.doi: 10.1088/1674-1056/27/10/106402

• CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES • 上一篇下一篇

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

收稿日期:2018-03-14 修回日期:2018-07-11 出版日期:2018-10-05 发布日期:2018-10-05
通讯作者: Qing-Kuan Meng, Dong-Tai Feng E-mail:qkmeng@sdut.edu.cn;fengdongtai@sdut.edu.cn
基金资助:
Project supported by the Natural Science Foundation of Shandong Province, China (Grant No. ZR2014EL002).

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

Received:2018-03-14 Revised:2018-07-11 Online:2018-10-05 Published:2018-10-05
Contact: Qing-Kuan Meng, Dong-Tai Feng E-mail:qkmeng@sdut.edu.cn;fengdongtai@sdut.edu.cn
Supported by:
Project supported by the Natural Science Foundation of Shandong Province, China (Grant No. ZR2014EL002).

摘要/Abstract

摘要：

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.

关键词: fractal scale-free network, phase transition, renormalization

Abstract:

Key words: fractal scale-free network, phase transition, renormalization

中图分类号: (Fractal and multifractal systems)

64.60.al

64.60.-i (General studies of phase transitions) 89.75.-k (Complex systems)

孟庆宽, 冯东太, 孙玉萍, 周爱萍, 孙艳, 谭树刚, 高绪团. Study on the phase transition of the fractal scale-free networks[J]. 中国物理B, 2018, 27(10): 106402-106402.

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[J]. Chin. Phys. B, 2018, 27(10): 106402-106402.

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

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

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