Noise-induced phase transition in the Vicsek model through eigen microstate methodology

doi:10.1088/1674-1056/ad5aed

中国物理B ›› 2024, Vol. 33 ›› Issue (9): 90501-090501.doi: 10.1088/1674-1056/ad5aed

Noise-induced phase transition in the Vicsek model through eigen microstate methodology

Yongnan Jia(贾永楠), Jiali Han(韩佳丽), and Qing Li(李擎)†

School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China

收稿日期:2024-04-15 修回日期:2024-06-14 接受日期:2024-06-24 发布日期:2024-08-15
通讯作者: Qing Li E-mail:liqing@ies.ustb.edu.cn
基金资助:
This work was supported by the National Natural Science Foundation of China (Grant No. 62273033).

Noise-induced phase transition in the Vicsek model through eigen microstate methodology

Yongnan Jia(贾永楠), Jiali Han(韩佳丽), and Qing Li(李擎)†

School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China

Received:2024-04-15 Revised:2024-06-14 Accepted:2024-06-24 Published:2024-08-15
Contact: Qing Li E-mail:liqing@ies.ustb.edu.cn
Supported by:
This work was supported by the National Natural Science Foundation of China (Grant No. 62273033).

摘要/Abstract

摘要： This paper presents a comprehensive framework for analyzing phase transitions in collective models such as the Vicsek model under various noise types. The Vicsek model, focusing on understanding the collective behaviors of social animals, is known due to its discontinuous phase transitions under vector noise. However, its behavior under scalar noise remains less conclusive. Renowned for its efficacy in the analysis of complex systems under both equilibrium and non-equilibrium states, the eigen microstate method is employed here for a quantitative examination of the phase transitions in the Vicsek model under both vector and scalar noises. The study finds that the Vicsek model exhibits discontinuous phase transitions regardless of noise type. Furthermore, the dichotomy method is utilized to identify the critical points for these phase transitions. A significant finding is the observed increase in the critical point for discontinuous phase transitions with escalation of population density.

关键词: Vicsek model, phase transitions, eigen microstate method, noise

Abstract: This paper presents a comprehensive framework for analyzing phase transitions in collective models such as the Vicsek model under various noise types. The Vicsek model, focusing on understanding the collective behaviors of social animals, is known due to its discontinuous phase transitions under vector noise. However, its behavior under scalar noise remains less conclusive. Renowned for its efficacy in the analysis of complex systems under both equilibrium and non-equilibrium states, the eigen microstate method is employed here for a quantitative examination of the phase transitions in the Vicsek model under both vector and scalar noises. The study finds that the Vicsek model exhibits discontinuous phase transitions regardless of noise type. Furthermore, the dichotomy method is utilized to identify the critical points for these phase transitions. A significant finding is the observed increase in the critical point for discontinuous phase transitions with escalation of population density.

Key words: Vicsek model, phase transitions, eigen microstate method, noise

中图分类号: (Phase transitions: general studies)

05.70.Fh

87.80.-y (Biophysical techniques (research methods))

Yongnan Jia(贾永楠), Jiali Han(韩佳丽), and Qing Li(李擎). Noise-induced phase transition in the Vicsek model through eigen microstate methodology[J]. 中国物理B, 2024, 33(9): 90501-090501.

Yongnan Jia(贾永楠), Jiali Han(韩佳丽), and Qing Li(李擎). Noise-induced phase transition in the Vicsek model through eigen microstate methodology[J]. Chin. Phys. B, 2024, 33(9): 90501-090501.

参考文献

[1] Butt T, Mufti T, Humayun A, Rosenthal P B, Khan S, Khan S and Molloy J E 2010 J. Biol. Chem. 285 4964
[2] Herbert-Read J E, Perna A, Mann R P, Schaerf T M, Sumpter D J T and Ward A J W 2011 Proc. Natl. Acad. Sci. USA 108 18726
[3] Becco C, Vandewalle N, Delcourt J and Poncin P 2006 Physica A 367 487
[4] Ballerini M, Cabibbo N, Candelier R, Cavagna A, Cisbani E, Giardina I, Lecomte V, Orlandi A, Parisi G, Procaccini A, Viale M and Zdravkovic V 2008 Proc. Natl. Acad. Sci. USA 105 1232
[5] Nagy M, Kos Z, Biro D and Vicsek T 2010 Nature 464 890
[6] Dalmao F and Ordecki E 2011 SLAM J. Appl. Math. 71 1307
[7] Jia Y N and Vicsek T 2019 New J. Phys. 21 093048
[8] Du J M 2019 Appl. Math. Comput. 363 124629
[9] Wang C H and DeBeer S 2021 Chem. Soc. Rev. 50 8743
[10] Du J M and Wu Z R 2022 Appl. Math. Comput. 430 127295
[11] Du J M and Wu Z R 2024 Knowledge-Based Systems 284 111287
[12] Reynolds C W 1987 ACM Siggraph Comput. Graph. 21 25
[13] Vicsek T, Czirok A, Ben-Jacob E, Cohen I and Shochet O 1995 Phys. Rev. Lett. 75 1226
[14] Cucker F and Smale S 2007 IEEE Trans. Automat. Control 52 852
[15] Barbaro A B T, Canizo J A, Carrillo J A and Degond P 2015 Multiscale Modeling and Simulation 14 1063
[16] Pearce D J G and Turner M S 2014 New J. Phys. 16 082002
[17] Aldana M and Huepe C 2003 J. Stat. Phys. 112 135
[18] Barbaro A B T and Degond P 2014 Discrete and Continuous Dynamical Systems B 19 1249
[19] Escaff D and Delpiano R 2020 Chaos 30 083137
[20] Du G L and Ye F F 2022 Chin. Phys. B 31 086401
[21] Vahabli D and Vicsek T 2023 Commun. Phys. 6 56
[22] Binder K 1981 Z. Phys. B 43 119
[23] Grégoire G and Chate H 2004 Phys. Rev. Lett. 92 025702
[24] Nagy M, Duruka I and Vicsek T 2007 Physica A 373 445
[25] Baglietto G and Albano E V 2009 Phys. Rev. E 80 050103
[26] Sun Y, Hu G K, Zhang Y W, Lu B, Lu Z H, Fan J F, Li X T, Deng Q M and Chen X S 2021 Commun. Theor. Phys. 73 065603
[27] Li X, Xue T T, Sun Y, Fan J F, Li H, Liu M X, Han Z G, Di Z R and Chen X S 2021 Chin. Phys. B 30 128703
[28] Hadamard J 1906 Bull. Am. Math. Soc. 12 194
[29] Strang G 1993 Am. Math. Mon. 100 848
[30] Lutz H O, Stein J, Datz S and Moak C D 1972 Phys. Rev. Lett. 28 8
[31] Privman V and Fisher M E 1984 Phys. Rev. B 30 322
[32] Privman V, Aharony A and Hohenberg P C 1991 Phase Transitions and Critical Phenomena (New York: Academic Press)
[33] Hu G K, Liu T, Liu M X, Chen W and Chen X S 2019 Sci. China Phys. Mech. Astron. 62 990511

Noise-induced phase transition in the Vicsek model through eigen microstate methodology

Noise-induced phase transition in the Vicsek model through eigen microstate methodology

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Ying Jing(景颖), Youguo Wang(王友国), Qiqing Zhai(翟其清), and Xianli Sun(孙先莉). Dynamic properties of rumor propagation model induced by Lévy noise on social networks[J]. 中国物理B, 2024, 33(9): 90203-090203.
[2]	Xiao-Zhen Yan(颜小珍), Xing-Zi Zhou(周幸姿), Chao-Fei Liu(刘超飞), Yin-Li Xu(徐寅力), Yi-Bin Huang(黄毅斌), Xiao-Wei Sheng(盛晓伟), and Yang-Mei Chen(陈杨梅). First-principles study on stability and superconductivity of ternary hydride LaYH_x (x =2, 3, 6 and 8)[J]. 中国物理B, 2024, 33(8): 86301-086301.
[3]	Yu-Chen Hu(胡雨辰) and Liang-Bin Hu(胡梁宾). Effect of the mixing of s-wave and chiral p-wave pairings on electrical shot noise properties of normal metal/superconductor tunnel junctions[J]. 中国物理B, 2024, 33(7): 77202-077202.
[4]	Haoran Yan(严浩然), Jiaqi Yan(颜家琦), Lianchun Yu(俞连春), and Yu-Feng Shao(邵玉峰). Cooperative activation of sodium channels for downgrading the energy efficiency in neuronal information processing[J]. 中国物理B, 2024, 33(5): 58801-058801.
[5]	Tai-Hao Cui(崔太豪), Ya-Qi Wei(魏雅琪), Ji Li(李冀), Quan Yuan(袁泉), Shuang-Qing Dai(戴双晴), Pei-Dong Li(李沛东), Fei Zhou(周飞), Jian-Qi Zhang(张建奇), Zhu-Jun Zheng(郑驻军), Liang Chen(陈亮), and Mang Feng(冯芒). Building and characterizing a stylus ion-trap system[J]. 中国物理B, 2024, 33(4): 43701-043701.
[6]	Heng Zhu(朱恒), Hongchao Shi(施洪潮), Zhengguo Tang(唐政国), and Bing Tang(唐炳). Interacting topological magnons in a checkerboard ferromagnet[J]. 中国物理B, 2024, 33(3): 37503-037503.
[7]	Kao Jia(贾考), Lan Hu(胡兰), and Linru Nie(聂林如). Symmetric Brownian motor subjected to Lévy noise[J]. 中国物理B, 2024, 33(2): 20502-020502.
[8]	Xue Deng(邓雪), Xiang Zhang(张翔), Qi Zang(臧琦), Dong-Dong Jiao(焦东东), Dan Wang(王丹), Jie Liu(刘杰), Jing Gao(高静), Guan-Jun Xu (许冠军), Rui-Fang Dong(董瑞芳), Tao Liu(刘涛), and Shou-Gang Zhang(张首刚). Coherent optical frequency transfer via 972-km fiber link[J]. 中国物理B, 2024, 33(2): 20602-020602.
[9]	Xun Yan(晏询), Zhijun Li(李志军), and Chunlai Li(李春来). Dynamics and synchronization in a memristor-coupled discrete heterogeneous neuron network considering noise[J]. 中国物理B, 2024, 33(2): 28705-028705.
[10]	Shu-Yuan Yang(杨舒媛), Jin-Chuan Hou(侯晋川), and Kan He(贺衎). Sharing quantum nonlocality in the noisy scenario[J]. 中国物理B, 2024, 33(1): 10302-10302.
[11]	Shumeng Chen(陈书梦), Sifan Ding(丁思凡), Zhen-Tao Zhang(张振涛), and Dong E. Liu(刘东). Majorana noise model and its influence on the power spectrum[J]. 中国物理B, 2024, 33(1): 17101-17101.
[12]	Li-Na Luan(栾丽娜), Mei-Yu Zhang(张镁玉), and Lin-Cheng Wang(王林成). Floquet dynamical quantum phase transitions in transverse XY spin chains under periodic kickings[J]. 中国物理B, 2023, 32(9): 90302-090302.
[13]	Xixian Zhang(张希贤) and Hao Hu(胡皓). Phase behavior and percolation in an equilibrium system of symmetrically interacting Janus disks on the triangular lattice[J]. 中国物理B, 2023, 32(8): 80502-080502.
[14]	Yang-Yang Fan(范洋洋), Jing Wang(王晶), Feng-Xia Hu(胡凤霞), Bao-He Li(李宝河), Ai-Cong Geng(耿爱丛), Zhuo Yin(殷卓), Cheng Zhang(张丞), Hou-Bo Zhou(周厚博), Meng-Qin Wang(王梦琴), Zi-Bing Yu(尉紫冰), and Bao-Gen Shen(沈保根). Low-temperature ferromagnetism in tensile-strained LaCoO_2.5 thin film[J]. 中国物理B, 2023, 32(8): 87504-087504.
[15]	Jiangling Liu(刘江令), Chaorun Li(李朝润), Hailing Gao(高海玲), and Luchun Du(杜鲁春). Vibrational resonance in globally coupled bistable systems under the noise background[J]. 中国物理B, 2023, 32(7): 70502-070502.