A new universality class describes Vicsek's flocking phase in physical dimensions

Abstract

The Vicsek simulation model of flocking together with its theoretical treatment by Toner and Tu in 1995 were two foundational cornerstones of active matter physics. However, despite the field's tremendous progress, the actual universality class (UC) governing the scaling behavior of Viscek's "flocking" phase remains elusive. Here, we use nonperturbative, functional renormalization group methods to analyze, numerically and analytically, a simplified version of the Toner-Tu model, and uncover a novel UC with scaling exponents that agree remarkably well with the values obtained in a recent simulation study by Mahault et al. [Phys. Rev. Lett. 123, 218001 (2019)], in both two and three spatial dimensions. We therefore believe that there is strong evidence that the UC uncovered here describes Vicsek's flocking phase.

Main text: 6 pages, 2 figures Supplemental Material: 12 pages, 3 figures

References in corpus (33)

• Novel type of phase transition in a system of self-driven particles
• Exact evolution equation for the effective potential
• Flocks, herds, and schools: A quantitative theory of flocking
• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• The Exact Renormalisation Group and Approximate Solutions
• Onset of collective and cohesive motion
• The nonperturbative functional renormalization group and its applications
• An Introduction to the Nonperturbative Renormalization Group
• Flow Equations for N Point Functions and Bound States
• A Reanalysis of the Hydrodynamic Theory of Fluid, Polar-Ordered Flocks
• General framework of the non-perturbative renormalization group for non-equilibrium steady states
• Birth, Death and Flight: A Theory of Malthusian Flocks
• Surprising mappings of 2D polar active fluids to 2D soap and 1D sandblasting
• Quantitative Assessment of the Toner and Tu Theory of Polar Flocks
• Critical Phenomenon of the Order-Disorder Transition in Incompressible Flocks
• Swarming in the Dirt: Ordered Flocks with Quenched Disorder
• Momentum Scale Expansion of Sharp Cutoff Flow Equations
• Infrared behavior in systems with a broken continuous symmetry: classical O(N) model vs interacting bosons
• Natural Swarms in $3.99$ Dimensions
• Hydrodynamic Theory of Flocking in the Presence of Quenched Disorder
• Nonequilibrium polarity-induced mechanism for chemotaxis: emergent Galilean symmetry and exact scaling exponents
• Fully developed isotropic turbulence: symmetries and exact identities
• Small Obstacle in a Large Polar Flock
• Incompressible polar active fluids in the moving phase
• Moving, reproducing, and dying beyond Flatland: Malthusian flocks in dimensions $d>2$
• Metastability of Discrete-Symmetry Flocks
• A novel nonequilibrium state of matter: a $d=4-\epsilon$ expansion study of Malthusian flocks
• Packed swarms on dirt: two-dimensional incompressible flocks with quenched and annealed disorder
• Hydrodynamic theory of two-dimensional incompressible polar active fluids with quenched and annealed disorder
• Novel critical phenomena in compressible polar active fluids: Dynamical and Functional Renormalization Group Studies
• Squeezed in three dimensions, moving in two: Hydrodynamic theory of 3D incompressible easy-plane polar active fluids
• Incompressible polar active fluids with quenched disorder in dimensions $d>2$
• Dynamics of packed swarms: time-displaced correlators of two dimensional incompressible flocks

Cited by in corpus (5)

• Minimum scaling model and exact exponents for the Nambu-Goldstone modes in the Vicsek Model
• Minimal mechanism for flocking in phoretically interacting active particles
• The Hamiltonian mechanics of exotic particles
• New universality classes govern the critical and multicritical behavior of an active Ising model
• Critical Motility-Induced Phase Separation in Three Dimensions is Consistent with Ising Universality