Phase transitions in swarming systems: A recent debate

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.

18 pages, 16 figures

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• Phase transitions, hysteresis, and hyperbolicity for self-organized alignment dynamics
• A review of active matter reviews
• Patterns, transitions and the role of leaders in the collective dynamics of a simple robotic flock
• Criticality and the Onset of Ordering in the Standard Vicsek Model
• Towards a quantitative kinetic theory of polar active matter
• Active matter beyond mean-field: Ring-kinetic theory for self-propelled particles
• Complex Network Structure of Flocks in the Standard Vicsek Model
• The escape problem for active particles confined to a disc
• Testing a thermodynamic approach to collective animal behavior in laboratory fish schools
• Gregarious vs Individualistic Behavior in Vicsek Swarms and the Onset of First-Order Phase Transitions
• Equilibrium to off-equilibrium crossover in homogeneous active matter
• The microscopic phase density functional approach to the construction of the kinetic and hydrodynamic description for the system of self-propelled particles
• Density-Independent Model of Self-Propelled Particles
• Capturing pattern bi-stability dynamics in delay-coupled swarms
• Transport coefficients of self-propelled particles. II. Numerics for vorticity fluctuations and the reverse perturbation method
• Bulk topological states in a new collective dynamics model
• Phase transitions on a class of generalized Vicsek-like models of collective motion
• Transport coefficients of self-propelled particles: Reverse perturbations and transverse current correlations
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• Keeping speed and distance for aligned motion
• Self-Propelled Collective Motion with Multiplicative Scalar Noise
• Flocking and spreading dynamics in populations of self-propelled agents
• A note on phase transitions for the Smoluchowski equation with dipolar potential