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New aspects of the continuous phase transition in the scalar noise model (SNM) of collective motion

Author

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  • Nagy, Máté
  • Daruka, István
  • Vicsek, Tamás

Abstract

In this paper we present our detailed investigations on the nature of the phase transition in the scalar noise model (SNM) of collective motion. Our results confirm the original findings of Vicsek et al. [Phys. Rev. Lett. 75 (1995) 1226] that the disorder–order transition in the SNM is a continuous, second order phase transition for small particle velocities (v⩽0.1). However, for large velocities (v⩾0.3) we find a strong anisotropy in the particle diffusion in contrast with the isotropic diffusion for small velocities. The interplay between the anisotropic diffusion and the periodic boundary conditions leads to an artificial symmetry breaking of the solutions (directionally quantized density waves) and a consequent first order transition like behavior. Thus, it is not possible to draw any conclusion about the physical behavior in the large particle velocity regime of the SNM.

Suggested Citation

  • Nagy, Máté & Daruka, István & Vicsek, Tamás, 2007. "New aspects of the continuous phase transition in the scalar noise model (SNM) of collective motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 373(C), pages 445-454.
    • Handle: RePEc:eee:phsmap:v:373:y:2007:i:c:p:445-454
    DOI: 10.1016/j.physa.2006.05.035
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    Cited by:

    1. Chepizhko, Oleksandr & Kulinskii, Vladimir, 2014. "The hydrodynamic description for the system of self-propelled particles: Ideal Viscek fluid," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 415(C), pages 493-502.
    2. Chen, Zhuo & Gao, Jianxi & Cai, Yunze & Xu, Xiaoming, 2011. "Evolution of cooperation among mobile agents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(9), pages 1615-1622.
    3. García Cantú Ros, A. & Antonopoulos, Ch.G. & Basios, V., 2011. "Emergence of coherent motion in aggregates of motile coupled maps," Chaos, Solitons & Fractals, Elsevier, vol. 44(8), pages 574-586.

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