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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 |
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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.
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Received: 14 March 2018
Revised: 11 July 2018
Accepted manuscript online:
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PACS:
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64.60.al
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(Fractal and multifractal systems)
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64.60.-i
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(General studies of phase transitions)
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89.75.-k
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(Complex systems)
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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
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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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[1] |
Albert R and Barabási A L 2002 Rev. Mod. Phys. 74 47
|
[2] |
Watts D J and Strogatz S H 1998 Nature 393 440
|
[3] |
Jiao B and Wu X Q 2017 Chin. Phys. B 26 028901
|
[4] |
Barabási A L and Albert R 1999 Science 286 509
|
[5] |
Liu H R, Dong M R, Yin R R and Han L 2015 Chin. Phys. B 24 050506
|
[6] |
Ravasz E, Somera A L, Mongru D A, Oltvai Z N and Barabási A L 2002 Science 297 1551
|
[7] |
Song C, Havlin S and Makse H A 2005 Nature 433 392
|
[8] |
Song C, Gallos L K, Havlin S and Makse H A 2007 J. Statist. Mech.:Theory and Experiment P03006
|
[9] |
Albert R, Jeong H and Barabási A L 1999 Nature 401 130
|
[10] |
Jeong H, Tombor B, Albert R, Oltvai Z N and Barabási A L 2000 Nature 407 651
|
[11] |
Database of Interacting Proteins http://dip.doe-mbi.ucla.edu/dip/
|
[12] |
Song C, Havlin S and Makse H A 2006 Nat. Phys. 2 275
|
[13] |
Lacasa L and Gómez-Gardeñes J 2013 Phys. Rev. Lett. 110 168703
|
[14] |
Shanker O 2007 Mod. Phys. Lett. B 21 321
|
[15] |
Shanker O 2007 Mod. Phys. Lett. B 21 639
|
[16] |
Dorogovtsev S N, Goltsev A V and Mendes J F F 2002 Phys. Rev. E 66 016104
|
[17] |
Leone M, Vázquez A, Vespignani A and Zecchina R 2002 Eur. Phys. J. B 28 191
|
[18] |
Aleksiejuka A, Holysta J A and Stauffer D 2002 Physica A 310 260
|
[19] |
Herrero C P 2004 Phys. Rev. E 69 067109
|
[20] |
Yi H 2010 Phys. Rev. E 81 012103
|
[21] |
Yi H 2015 Phys. Rev. E 91 012146
|
[22] |
Yoon S, Sindaci M S, Goltsev A V and Mendes J F F 2015 Phys. Rev. E 91 032814
|
[23] |
Herrero C P 2015 Phys. Rev. E 91 052812
|
[24] |
Jedrzejewski A, Chmiel A and Sznajd-Weron K 2017 Phys. Rev. E 96 012132
|
[25] |
Rozenfeld H D, Song C and Makse H A 2010 Phys. Rev. Lett. 104 025701
|
[26] |
Goh K I, Salvi G, Kahng B and Kim D 2006 Phys. Rev. Lett. 96 018701
|
[27] |
Harris T E 1963 Theory of Branching Processes (Berlin:Springer-Verlag)
|
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