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

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

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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