New aspects of the continuous phase transition in the scalar noise model (SNM) of collective motion

Abstract

In this paper we present our detailed investigations on the nature of the phase transition in the scalar noise model (SNM) of collective motion. Our results confirm the original findings of Vicsek et al. [Phys. Rev. Lett. 75 (1995) 1226] that the disorder-order transition in the SNM is a continuous, second order phase transition for small particle velocities ($v\le 0.1$). However, for large velocities ($v\ge 0.3$) we find a strong anisotropy in the particle diffusion in contrast with the isotropic diffusion for small velocities. The interplay between the anisotropic diffusion and the periodic boundary conditions leads to an artificial symmetry breaking of the solutions (directionally quantized density waves) and a consequent first order transition like behavior. Thus, it is not possible to draw any conclusion about the physical behavior in the large particle velocity regime of the SNM.

13 pages, 11 figures

References in corpus (2)

• Novel type of phase transition in a system of self-driven particles
• Spontaneously ordered motion of self-propelled particles

Cited by in corpus (32)

• Collective motion of self-propelled particles interacting without cohesion
• Phase transition in the collective migration of tissue cells: experiment and model
• State Transitions and the Continuum Limit for a 2D Interacting, Self-Propelled Particle System
• Finite-size scaling as a way to probe near-criticality in natural swarms
• A mean-field theory for self-propelled particles interacting by velocity alignment mechanisms
• Adaptive-network models of swarm dynamics
• Phase transitions in swarming systems: A recent debate
• Kinetic theory for systems of self-propelled particles with metric-free interactions
• Optimal View Angle in Collective Dynamics of Self-propelled Agents
• Mutual Information as a Tool for Identifying Phase Transitions in Dynamical Complex Systems With Limited Data
• Evolution of Cooperation among Mobile Agents
• Turning with the others: novel transitions in an SPP model with coupling of accelerations
• Phase transitions induced by complex nonlinear noise in a system of self-propelled agents
• Criticality and the Onset of Ordering in the Standard Vicsek Model
• Phase transition in the scalar noise model of collective motion in three dimensions
• Active matter beyond mean-field: Ring-kinetic theory for self-propelled particles
• Density regulation in strictly metric-free swarms
• Coarsening Dynamics in the Vicsek Model of Active Matter
• Estimation of the critical behavior in an active colloidal system with Vicsek-like interactions
• Vicsek Model by Time-Interlaced Compression: a Dynamical Computable Information Density
• Numerical simulations of a non-conservative hyperbolic system with geometric constraints describing swarming behavior
• Pattern formation and phase transition in the collective dynamics of a binary mixture of polar self-propelled particles
• Bond disorder enhances the information transfer in polar flock
• Detecting and characterizing phase transitions in active matter using entropy
• Keeping speed and distance for aligned motion
• Gaussian theory for spatially distributed self-propelled particles
• Self-Propelled Collective Motion with Multiplicative Scalar Noise
• Active Matter Flocking via Predictive Alignment
• Universality in Incompressible Active Fluid: Effect of Non-local Shear Stress
• Flocking and spreading dynamics in populations of self-propelled agents
• Traveling Fronts and the Smoothing of the Collective-Motion Phase Transition in Vibrated Polar Disks
• Local disalignment can promote coherent collective motion through rapid information transfer