Abstract.
We consider disorder-order phase transitions in the three-dimensional version of the scalar noise model (SNM) of flocking. Our results are analogous to those found for the two-dimensional case [CITE]. For small velocity (v≤0.1) a continuous, second-order phase transition is observable, with the diffusion of nearby particles being isotropic. By increasing the particle velocities the phase transition changes to first order, and the diffusion becomes anisotropic. The first-order transition in the latter case is probably caused by the interplay between anisotropic diffusion and periodic boundary conditions, leading to a boundary condition dependent symmetry breaking of the solutions.
Similar content being viewed by others
References
M. Nagy, I. Daruka, T. Vicsek, Physica A 373, 445 (2007)
T. Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen, O. Shochet, Phys. Rev. Lett. 75, 1226 (1995)
A. Czirók, H.E. Stanley, T. Vicsek, J. Phys. A 30, 1375 (1997)
Z. Csahók, T. Vicsek, Phys. Rev. E 52, 5297 (1995)
J. Toner, Y. Tu, Phys. Rev. Lett. 75, 4326 (1995)
J. Toner, Y. Tu, M. Ulm, Phys. Rev. Lett. 80, 4819 (1998)
J. Toner, Y. Tu, Phys. Rev. E 58, 4828 (1998)
A. Czirók, M. Vicsek, T. Vicsek, Physica A 264, 299 (1999)
G. Grégoire, H. Chaté, Phys. Rev. Lett. 92, 025702 (2004)
J.K. Parrish, W.M. Hammer, Animal Groups in Three Dimensions (Cambridge University Press, Cambridge, 1997)
C.J. Feare, The Starlings (Oxford University Press, 1984); J.K. Parrish, W.H. Hamner (eds.), Animal Groups in Three Dimensions (Cambridge University Press, Cambridge, 1997); C.W. Reynolds, Comp. Graph. 21, 25 (1987)
J.K. Parrish, L. Edelstein-Keshet, Science 284, 99 (1999); T. Inagaki, W. Sakamoto, T. Kuroki, Bull. Jap. Soc. Sci. Fish 42, 265 (1976)
E.M. Rauch, M.M. Millonas, D.R. Chialvo, Phys. Lett. A 207, 185 (1995)
E. Ben-Jacob, I. Cohen, O. Shochet, A. Czirók, T. Vicsek, Phys. Rev. Lett. 75, 2899 (1995); Bacteria as Multicellular Organisms, edited by J.A. Shapiro, BioEssays 17, 597 (1995); J.A. Shapiro, M. Dworkin (Oxford University Press, 1997)
K. Binder, D.W. Herrmann, Monte Carlo Simulation in Statistical Physics (Springer, 1997)
C. Huepe, M. Aldana, Phys. Rev. Lett. 92, 168701 (2004)
M. Aldana, V. Dossetti, C. Huepe, V.M. Kenkre, H. Larralde, Phys. Rev. Lett. 98, 095702 (2007)
G. Grégoire, H. Chaté, Y. Tu, Phys. Rev. E 64, 011902 (2001)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Gönci, B., Nagy, M. & Vicsek, T. Phase transition in the scalar noise model of collective motion in three dimensions. Eur. Phys. J. Spec. Top. 157, 53–59 (2008). https://doi.org/10.1140/epjst/e2008-00630-2
Issue Date:
DOI: https://doi.org/10.1140/epjst/e2008-00630-2