A new universality class describes Vicsek's flocking phase in physical dimensions
arxiv(2024)
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.
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