| CROSS-DISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY |
|
|
|
|
Phase Transitions of Majority-Vote Model on Modular Networks |
| HUANG Feng1, CHEN Han-Shuang2**, SHEN Chuan-Sheng3 |
1School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601
2School of Physics and Material Science, Anhui University, Hefei 230601
3Department of Physics, Anqing Normal University, Anqing 246011
|
|
| Cite this article: |
|
HUANG Feng, CHEN Han-Shuang, SHEN Chuan-Sheng 2015 Chin. Phys. Lett. 32 118902 |
|
|
|
|
Abstract We investigate the phase transitions behavior of the majority-vote model with noise on a topology that consists of two coupled random networks. A parameter p is used to measure the degree of modularity, defined as the ratio of intermodular to intramodular connectivity. For the networks of strong modularity (small p), as the level of noise f increases, the system undergoes successively two transitions at two distinct critical noises, fc1 and fc2. The first transition is a discontinuous jump from a coexistence state of parallel and antiparallel order to a state that only parallel order survives, and the second one is continuous that separates the ordered state from a disordered state. As the network modularity worsens, fc1 becomes smaller and fc2 does not change, such that the antiparallel ordered state will vanish if p is larger than a critical value of pc. We propose a mean-field theory to explain the simulation results.
|
|
|
Received: 10 August 2015
Published: 01 December 2015
|
|
| PACS: |
89.75.Hc
|
(Networks and genealogical trees)
|
| |
05.45.-a
|
(Nonlinear dynamics and chaos)
|
| |
64.60.Cn
|
(Order-disorder transformations)
|
|
|
|
|
|
[1] Dorogovtsev S N, Goltseve A V and Mendes J F F 2008 Rev. Mod. Phys. 80 1275
[2] Castellano C, Fortunato S and Loreto V 2009 Rev. Mod. Phys. 81 591
[3] Stauffer D, Fortunato S and Loreto V 2008 Am. J. Phys. 76 470
[4] de Oliveira M J 1992 J. Stat. Phys. 66 273
[5] Pereira L F C and Moreira F G B 2005 Phys. Rev. E 71 016123
[6] Lima F W S, Sousa A and Sumuor M 2008 Physica A 387 3503
[7] Campos P R A, de Oliveira V M and Moreira F G B 2003 Phys. Rev. E 67 026104
[8] Luz E M S and Lima F W S 2007 Int. J. Mod. Phys. C 18 1251
[9] Stone T E and McKay S R 2015 Physica A 419 437
[10] Lima F W S 2006 Int. J. Mod. Phys. C 17 1257
[11] Lima F W S and Malarz K 2006 Int. J. Mod. Phys. C 17 1273
[12] Kwak W, Yang J S, Sohn Y I and Kim I M 2007 Phys. Rev. E 75 061110
[13] Yang J S, Kim I M and Kwak W 2008 Phys. Rev. E 77 051122
[14] Wu Z X and Holme P 2010 Phys. Rev. E 81 011133
[15] Santos J, Lima F and Malarz K 2011 Physica A 390 359
[16] Acu?a-Lara A L and Sastre F 2012 Phys. Rev. E 86 041123
[17] Acu?a-Lara A L, Sastre F and Vargas-Arriola J R 2014 Phys. Rev. E 89 052109
[18] Chen H, Shen C, He G, Zhang H and Hou Z 2015 Phys. Rev. E 91 022816
[19] Newman M E J 2006 Proc. Natl. Acad. Sci. USA 103 8577
[20] Fortunato S 2010 Phys. Rep. 486 75
[21] Arenas A, Díaz-Guilera A and Pérez-Vicente C J 2006 Phys. Rev. Lett. 96 114102
[22] Li D et al 2008 Phys. Rev. Lett. 101 168701
[23] Zhou C et al 2006 Phys. Rev. Lett. 97 238103
[24] Liu Z and Hu B 2005 Europhys. Lett. 72 315
[25] Zhou Y Z, Liu Z H and Zhou J 2007 Chin. Phys. Lett. 24 581
[26] Huang L, Park K and Lai Y C 2006 Phys. Rev. E 73 035103
[27] Nematzadeh A, Ferrara E, Flammini A and Ahn Y Y 2014 Phys. Rev. Lett. 113 088701
[28] Lambiotte R and Ausloos M 2007 J. Stat. Mech. 2007 P08026
[29] Lambiotte R, Ausloos M and Ho?yst J A 2007 Phys. Rev. E 75 030101
[30] Wang R and Chi L P 2007 Chin. Phys. Lett. 24 1502
[31] Pan R K and Sinha S 2009 Europhys. Lett. 85 68006
[32] Dasgupta S, Pan R K and Sinha S 2009 Phys. Rev. E 80 025101(R)
[33] Suchecki K and Ho?yst J A 2009 Phys. Rev. E 80 031110
[34] Chen H and Hou Z 2011 Phys. Rev. E 83 046124
[35] Zhou H and Lipowsky R 2005 Proc. Natl. Acad. Sci. USA 102 10052
[36] Castellano C and Pastor-Satorras R 2006 J. Stat. Mech. 2006 P05001 |
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
