Noisy multistate voter model for flocking in finite dimensions.
Phys Rev E
; 104(3-1): 034111, 2021 Sep.
Article
em En
| MEDLINE
| ID: mdl-34654099
We study a model for the collective behavior of self-propelled particles subject to pairwise copying interactions and noise. Particles move at a constant speed v on a two-dimensional space and, in a single step of the dynamics, each particle adopts the direction of motion of a randomly chosen neighboring particle within a distance R=1, with the addition of a perturbation of amplitude η (noise). We investigate how the global level of particles' alignment (order) is affected by their motion and the noise amplitude η. In the static case scenario v=0 where particles are fixed at the sites of a square lattice and interact with their first neighbors, we find that for any noise η>0 the system reaches a steady state of complete disorder in the thermodynamic limit, while for η=0 full order is eventually achieved for a system with any number of particles N. Therefore, the model displays a transition at zero noise when particles are static, and thus there are no ordered steady states for a finite noise (η>0). We show that the finite-size transition noise vanishes with N as η_{c}^{1D}â¼N^{-1} and η_{c}^{2D}â¼(NlnN)^{-1/2} in one- and two-dimensional lattices, respectively, which is linked to known results on the behavior of a type of noisy voter model for catalytic reactions. When particles are allowed to move in the space at a finite speed v>0, an ordered phase emerges, characterized by a fraction of particles moving in a similar direction. The system exhibits an order-disorder phase transition at a noise amplitude η_{c}>0 that is proportional to v, and that scales approximately as η_{c}â¼v(-lnv)^{-1/2} for vâª1. These results show that the motion of particles is able to sustain a state of global order in a system with voter-like interactions.
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1
Coleções:
01-internacional
Base de dados:
MEDLINE
Idioma:
En
Revista:
Phys Rev E
Ano de publicação:
2021
Tipo de documento:
Article
País de afiliação:
Argentina
País de publicação:
Estados Unidos