Statistical properties of swarms of self-propelled particles with repulsions across the order-disorder transition

TL;DR

This paper investigates how self-propelled particles with repulsive interactions transition between ordered and disordered states, revealing new phase behavior and critical properties through simulations.

Contribution

It introduces a modified Vicsek model with repulsions, demonstrating a novel density-dependent transition to disorder and analyzing correlation functions and critical exponents.

Findings

Discovered a transition to a disordered phase at high densities due to repulsions.

Identified algebraic decay of velocity correlations in the ordered phase.

Found that the critical exponent becomes universal at high densities.

Abstract

We study dynamic self-organisation and order-disorder transitions in a two-dimensional system of self-propelled particles. Our model is a variation of the Vicsek model, where particles align the motion to their neighbours but repel each other at short distances. We use computer simulations to measure the orientational order parameter for particle velocities as a function of intensity of internal noise or particle density. We show that in addition to the transition to an ordered state on increasing the particle density, as reported previously, there exists a transition into a disordered phase at the higher densities, which can be attributed to the destructive action of the repulsions. We demonstrate that the transition into the ordered phase is accompanied by the onset of algebraic behaviour of the two-point velocity correlation function and by a non-monotonous variation of the velocity relaxation time. The critical exponent for the decay of the velocity correlation function in the ordered phase depends on particle concentration at low densities but assumes a universal value in more dense systems.