Fluctuation-induced first order transition to collective motion

Abstract The nature of the transition to collective motion in assemblies of aligning self-propelled particles remains a long-standing matter of debate. In this article, we focus on dry active matter and show that weak fluctuations suffice to generically turn second-order mean-field transitions into...

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Bibliographic Details
Published in:Journal of statistical mechanics 2024-08, Vol.2024 (8), p.84003
Main Authors: Martin, David, Spera, Gianmarco, Chaté, Hugues, Duclut, Charlie, Nardini, Cesare, Tailleur, Julien, van Wijland, Frédéric
Format: Article
Language:English
Subjects:
active matter
non-equilibirum processes
statistical physics
Stochastic dynamics
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Summary:Abstract The nature of the transition to collective motion in assemblies of aligning self-propelled particles remains a long-standing matter of debate. In this article, we focus on dry active matter and show that weak fluctuations suffice to generically turn second-order mean-field transitions into a ‘discontinuous’ coexistence scenario. Our theory shows how fluctuations induce a density-dependence of the polar-field mass, even when this effect is absent at mean-field level. In turn, this dependency on density triggers a feedback loop between ordering and advection that ultimately leads to an inhomogeneous transition to collective motion and the emergence of inhomogeneous travelling bands. Importantly, we show that such a fluctuation-induced first order transition is present in both metric models, in which particles align with neighbors within a finite distance, and in ‘topological’ ones, in which alignment is based on more complex constructions of neighbor sets. We compute analytically the noise-induced renormalization of the polar-field mass using stochastic calculus, which we further back up by a one-loop field-theoretical analysis. Finally, we confirm our analytical predictions by numerical simulations of fluctuating hydrodynamics as well as of topological particle models with either k -nearest neighbors or Voronoi alignment.
ISSN:1742-5468
1742-5468
DOI:10.1088/1742-5468/ad6428