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 (6)

• Novel type of phase transition in a system of self-driven particles
• Exact evolution equation for the effective potential
• Critical Phenomenon of the Order-Disorder Transition in Incompressible Flocks
• Fully developed isotropic turbulence: symmetries and exact identities
• Small Obstacle in a Large Polar Flock
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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