Noisy multistate voter model for flocking in finite dimensions

Ernesto S. Loscar, Gabriel Baglietto, and Federico Vazquez
Phys. Rev. E 104, 034111 – Published 8 September 2021

Abstract

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 ηc1DN1 and ηc2D(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 ηc>0 that is proportional to v, and that scales approximately as ηcv(lnv)1/2 for v1. 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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  • Received 26 January 2021
  • Accepted 25 August 2021

DOI:https://doi.org/10.1103/PhysRevE.104.034111

©2021 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsInterdisciplinary Physics

Authors & Affiliations

Ernesto S. Loscar and Gabriel Baglietto

  • Instituto de Física de Líquidos y Sistemas Biológicos (IFLYSIB), UNLP, CCT La Plata–CONICET, Calle 59 no. 789, B1900BTE La Plata, Argentina

Federico Vazquez*

  • Instituto de Cálculo, FCEN, Universidad de Buenos Aires and CONICET, C1428EGA Buenos Aires, Argentina

  • *fede.vazmin@gmail.com

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Issue

Vol. 104, Iss. 3 — September 2021

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