Phase transitions in swarming systems: A recent debate

TL;DR

This paper reviews the debate on whether the phase transition in the Vicsek model of swarming is continuous or discontinuous, presenting new numerical evidence suggesting boundary conditions may influence observed transition order.

Contribution

It provides a comprehensive review of the ongoing debate and introduces new numerical results indicating boundary effects may cause apparent discontinuities.

Findings

Boundary conditions can create artifacts mimicking discontinuous transitions

Numerical results suggest the transition may be inherently continuous

The debate remains open with evidence supporting both perspectives

Abstract

In this work we consider the phase transition from ordered to disordered states that occur in the Vicsek model of self-propelled particles. This model was proposed to describe the emergence of collective order in swarming systems. When noise is added to the motion of the particles, the onset of collective order occurs through a dynamical phase transition. Based on their numerical results, Vicsek and his colleagues originally concluded that this phase transition was of second order (continuous). However, recent numerical evidence seems to indicate that the phase transition might be of first order (discontinuous), thus challenging Vicsek's original results. In this work we review the evidence supporting both aspects of this debate. We also show new numerical results indicating that the apparent discontinuity of the phase transition may in fact be a numerical artifact produced by the artificial periodicity of the boundary conditions.