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 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 , with the addition of a perturbation of amplitude (noise). We investigate how the global level of particles' alignment (order) is affected by their motion and the noise amplitude . In the static case scenario where particles are fixed at the sites of a square lattice and interact with their first neighbors, we find that for any noise the system reaches a steady state of complete disorder in the thermodynamic limit, while for full order is eventually achieved for a system with any number of particles . 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 (). We show that the finite-size transition noise vanishes with as and 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 , 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 that is proportional to , and that scales approximately as for . These results show that the motion of particles is able to sustain a state of global order in a system with voter-like interactions.
- Received 26 January 2021
- Accepted 25 August 2021
DOI:https://doi.org/10.1103/PhysRevE.104.034111
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