Finite density scaling laws of condensation phase transition in zero-range processes on scale-free networks

doi:10.1088/1674-1056/ab8a41

中国物理B ›› 2020, Vol. 29 ›› Issue (8): 88904-088904.doi: 10.1088/1674-1056/ab8a41

• SPECIAL TOPIC—Ultracold atom and its application in precision measurement • 上一篇

Finite density scaling laws of condensation phase transition in zero-range processes on scale-free networks

Guifeng Su(苏桂锋), Xiaowen Li(李晓温), Xiaobing Zhang(张小兵), Yi Zhang(张一)

1 Department of Physics, Shanghai Normal University, Shanghai 200234, China;
2 School of Physics, Nankai University, Tianjin 300071, China

收稿日期:2020-01-08 修回日期:2020-04-06 出版日期:2020-08-05 发布日期:2020-08-05
通讯作者: Yi Zhang E-mail:yizhang@shnu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11505115).

Finite density scaling laws of condensation phase transition in zero-range processes on scale-free networks

Guifeng Su(苏桂锋)¹, Xiaowen Li(李晓温)¹, Xiaobing Zhang(张小兵)², Yi Zhang(张一)¹

1 Department of Physics, Shanghai Normal University, Shanghai 200234, China;
2 School of Physics, Nankai University, Tianjin 300071, China

Received:2020-01-08 Revised:2020-04-06 Online:2020-08-05 Published:2020-08-05
Contact: Yi Zhang E-mail:yizhang@shnu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11505115).

摘要/Abstract

摘要： The dynamics of zero-range processes on complex networks is expected to be influenced by the topological structure of underlying networks. A real space complete condensation phase transition in the stationary state may occur. We study the finite density effects of the condensation transition in both the stationary and dynamical zero-range processes on scale-free networks. By means of grand canonical ensemble method, we predict analytically the scaling laws of the average occupation number with respect to the finite density for the steady state. We further explore the relaxation dynamics of the condensation phase transition. By applying the hierarchical evolution and scaling ansatz, a scaling law for the relaxation dynamics is predicted. Monte Carlo simulations are performed and the predicted density scaling laws are nicely validated.

关键词: finite density scaling, zero-range processes (ZRP), scale-free networks

Abstract: The dynamics of zero-range processes on complex networks is expected to be influenced by the topological structure of underlying networks. A real space complete condensation phase transition in the stationary state may occur. We study the finite density effects of the condensation transition in both the stationary and dynamical zero-range processes on scale-free networks. By means of grand canonical ensemble method, we predict analytically the scaling laws of the average occupation number with respect to the finite density for the steady state. We further explore the relaxation dynamics of the condensation phase transition. By applying the hierarchical evolution and scaling ansatz, a scaling law for the relaxation dynamics is predicted. Monte Carlo simulations are performed and the predicted density scaling laws are nicely validated.

Key words: finite density scaling, zero-range processes (ZRP), scale-free networks

中图分类号: (Networks and genealogical trees)

89.75.Hc

05.20.-y (Classical statistical mechanics) 02.50.Ey (Stochastic processes)

苏桂锋, 李晓温, 张小兵, 张一. Finite density scaling laws of condensation phase transition in zero-range processes on scale-free networks[J]. 中国物理B, 2020, 29(8): 88904-088904.

Guifeng Su(苏桂锋), Xiaowen Li(李晓温), Xiaobing Zhang(张小兵), Yi Zhang(张一). Finite density scaling laws of condensation phase transition in zero-range processes on scale-free networks[J]. Chin. Phys. B, 2020, 29(8): 88904-088904.

参考文献 39

[1]	Anderson M H, Ensher J R, Matthews M R, Wieman C E and Cornell E A 1995 Science 269 198 doi: 10.1126/science.269.5221.198
[2]	Chowdhury D, Santen L and Schadschneider A 2000 Phys. Rep. 329 199 doi: 10.1016/S0370-1573(99)00117-9
[3]	van der Meer D, van der Weele K and Lohse D 2002 Phys. Rev. Lett. 88 174302 doi: 10.1103/PhysRevLett.88.174302
[4]	van der Meer D, van der Weele K and Lohse D 2004 J. Stat. Mech.:Theor. Exp. 04 P04004
[5]	Krapivsky P L, Redner S and Leyvraz F 2000 Phys. Rev. Lett. 85 4629 doi: 10.1103/PhysRevLett.85.4629
[6]	Bianconi G and Barabási A L 2001 Phys. Rev. Lett. 86 5632 doi: 10.1103/PhysRevLett.86.5632
[7]	Su G F, Zhang X B and Zhang Y 2012 Eurphys. Lett. 100 38003 doi: 10.1209/0295-5075/100/38003
[8]	Pathria R K and Beale P D 2011 Statistical Mechanics 3rd edn (New York:Academic Press)
[9]	Liggett T M 1999 Stochastic Interacting Systems:Contact, Voter, and Exclusion Processes (Berlin:Springer)
[10]	Schmittmann B and Zia R K P 1995 Statistical Mechanics of Driven Diffusive Systems edited by Domb C and Lebowitz J L (New York:Academic Press)
[11]	Evans M R, Kafri Y, Koduvely H M and Mukamel D 1998 Phys. Rev. Lett. 80 425 doi: 10.1103/PhysRevLett.80.425
[12]	Evans M R Hanney T and Majumdar S N 2006 Phys. Rev. Lett. 97 010602 doi: 10.1103/PhysRevLett.97.010602
[13]	Spitzer F 1970 Adv. Math. 5 246 doi: 10.1016/0001-8708(70)90034-4
[14]	Evans M R and Hanney T 2005 J. Phys. A:Math. Gen. 38 R195
[15]	Godréche C 2007 Lect. Notes Phys. 716 261 doi: 10.1007/3-540-69684-9_6
[16]	Evans M R 2000 Braz. J. Phys. 30 42 doi: 10.1590/S0103-97332000000100005
[17]	Großkinsky S, Schütz G M and Spohn H 2003 J. Stat. Mech.:Theor. Exp. 113 389
[18]	Majumdar S N, Evans M R and Zia R K P 2005 Phys. Rev. Lett. 94 180601 doi: 10.1103/PhysRevLett.94.180601
[19]	Godréche C and Luck J M 2012 J. Stat. Mech.:Theor. Exp. 2012 P12013
[20]	Albert R and Barábasi A L 2002 Rev. Mod. Phys. 74 47 doi: 10.1103/RevModPhys.74.47
[21]	Eguiluz V M, Chialvo D R, Cecchi G A, Baliki M and Apkarian A V 2005 Phys. Rev. Lett. 94 018102 doi: 10.1103/PhysRevLett.94.018102
[22]	Boccaletti S, Latora V, Moreno Y, Chavez M and Hwang D U 2006 Phys. Rep. 424 175 doi: 10.1016/j.physrep.2005.10.009
[23]	Barabási A L and Albert R 1999 Science 286 509 doi: 10.1126/science.286.5439.509
[24]	Dorogovtsev S N, Goltsev A V and Mendes J F F 2008 Rev. Mod. Phys. 80 1275 doi: 10.1103/RevModPhys.80.1275
[25]	Barthelemy M, Barrat A, Pastor-Satorras R and Vespignani A 2004 Phys. Rev. Lett. 92 178701 doi: 10.1103/PhysRevLett.92.178701
[26]	Sood V and Redner S 2005 Phys. Rev. Lett. 94 178701 doi: 10.1103/PhysRevLett.94.178701
[27]	Noh J D, Shim G M and Lee H 2005 Phys. Rev. Lett. 94 198701 doi: 10.1103/PhysRevLett.94.198701
[28]	Noh J D 2005 Phys. Rev. E 72 056123 doi: 10.1103/PhysRevE.72.056123
[29]	Tang M, Liu Z and Zhou J 2006 Phys. Rev. E 74 036101 doi: 10.1103/PhysRevE.74.036101
[30]	Cohen R, Erez K, ben-Avraham D and Havlin S 2000 Phys. Rev. Lett. 85 4626 doi: 10.1103/PhysRevLett.85.4626
[31]	Noh J D and Rieger H 2004 Phys. Rev. Lett. 92 118701 doi: 10.1103/PhysRevLett.92.118701
[32]	Krug J 2000 Braz. J. Phys. 30 97 doi: 10.1590/S0103-97332000000100009
[33]	Evans M R 1996 Europhys. Lett. 36 13 doi: 10.1209/epl/i1996-00180-y
[34]	Jain K and Barma M 2003 Phys. Rev. Lett. 91 135701 doi: 10.1103/PhysRevLett.91.135701
[35]	Evans M R, Majumdar S N and Zia R K P 2004 J. Phys. A 37 L275
[36]	Zia R K P, Evans M R and Majumdar S N 2004 J. Stat. Mech.:Theor. Exp. 2004 L10001
[37]	Godréche C 2003 J. Phys. A:Math. Theor. 36 6313
[38]	Großkinsky S and Hanney T 2005 Phys. Rev. E 72 016129 doi: 10.1103/PhysRevE.72.016129
[39]	Godréche C and Drouffe J M 2017 J. Phys. A:Math. Theor. 50 015005 doi: 10.1088/1751-8113/50/1/015005

Finite density scaling laws of condensation phase transition in zero-range processes on scale-free networks

Finite density scaling laws of condensation phase transition in zero-range processes on scale-free networks

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