Phase transition in the scalar noise model of collective motion in three dimensions

TL;DR

This study investigates phase transitions in a 3D scalar noise model of flocking, revealing a shift from second-order to first-order transitions as particle velocity increases, with associated changes in diffusion behavior.

Contribution

It extends the understanding of phase transitions in the scalar noise model from two to three dimensions, highlighting the impact of particle velocity on transition order and diffusion anisotropy.

Findings

Second-order phase transition at low velocities with isotropic diffusion

Transition becomes first-order at higher velocities with anisotropic diffusion

Boundary conditions influence the symmetry breaking in the transition

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. 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.