Noisy multistate voter model for flocking in finite dimensions,Physical Review E

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Noisy multistate voter model for flocking in finite dimensions
Physical Review E ( IF 2.2 ) Pub Date : 2021-09-08 , DOI: 10.1103/physreve.104.034111
Ernesto S Loscar ₁ , Gabriel Baglietto ₁ , Federico Vazquez ₂

Affiliation

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

η_{c}^{1 D} \sim N^{- 1}

and

η_{c}^{2 D} \sim {(N ln N)}^{- 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