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Metastability of Discrete-Symmetry Flocks

Brieuc Benvegnen, Omer Granek, Sunghan Ro, Ran Yaacoby, Hugues Chaté, Yariv Kafri, David Mukamel, Alexandre Solon, and Julien Tailleur
Phys. Rev. Lett. 131, 218301 – Published 22 November 2023
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Abstract

We study the stability of the ordered phase of flocking models with a scalar order parameter. Using both the active Ising model and a hydrodynamic description, we show that droplets of particles moving in the direction opposite to that of the ordered phase nucleate and grow. We characterize analytically this self-similar growth and demonstrate that droplets spread ballistically in all directions. Our results imply that, in the thermodynamic limit, discrete-symmetry flocks—and, by extension, continuous-symmetry flocks with rotational anisotropy—are metastable in all dimensions.

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  • Received 1 June 2023
  • Accepted 23 October 2023

DOI:https://doi.org/10.1103/PhysRevLett.131.218301

© 2023 American Physical Society

Physics Subject Headings (PhySH)

Polymers & Soft MatterStatistical Physics & Thermodynamics

Authors & Affiliations

Brieuc Benvegnen1, Omer Granek2, Sunghan Ro3, Ran Yaacoby2, Hugues Chaté4,5,1, Yariv Kafri2, David Mukamel6, Alexandre Solon1, and Julien Tailleur3

  • 1Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée, 75005 Paris, France
  • 2Department of Physics, Technion–Israel Institute of Technology, Haifa 32000, Israel
  • 3Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
  • 4Service de Physique de l’Etat Condensé, CEA, CNRS, Université Paris-Saclay, CEA-Saclay, 91191 Gif-sur-Yvette, France
  • 5Computational Science Research Center, Beijing 100094, China
  • 6Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel

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Issue

Vol. 131, Iss. 21 — 24 November 2023

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Images

  • Figure 1
    Figure 1

    Simulations of the 2D AIM. (a),(b) Snapshots of the magnetization field following the introduction in the ordered phase of a counterpropagating droplet at x=y=t=0 (r=10, ρd0=5ρo), averaged over 100 runs. (c) Polarization (red) and density (black) profiles at y=0 for the snapshot shown in (b). (d) Reversal probability Pr(r) for ρd0=1.2ρo. The dotted line is a fit to a hyperbolic tangent used to extract rc. (e),(f) Variations of rc with T and D. (g) Average nucleation time τd in a system of size L×L. Parameters: v=1; D=1 [except for (g) where D=0.1]; ρo=10 (a)–(c), 5 (d)–(f), and 8 (g); β=2 [except for (f)]; (Lx,Ly)=(8000,800) in (a)–(c) and (200, 100) in (e),(f).

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  • Figure 2
    Figure 2

    (a) Snapshot of the m/ρo field obtained by integrating Eqs. (1) and (2) starting from a counterpropagating droplet introduced in the ordered phase solution at t=0 (initial radius r=10, initial droplet density ρd0=12ρo). Straight and parabolic green lines are guides to the eye. (b) Isodensity curves at ρ=(ρd+ρo)/2 in ballistically rescaled coordinates for microscopic (solid lines) and hydrodynamic (dashed lines) simulations. (c) Cross-sectional plots of the magnetization in PDE simulations along the maximal-width line shown in white in (a). (d) Positions of the front (xf) and rear (x+) droplet interfaces, and of the end of the comet (x) at y=0, together with the droplet width h. Symbols and lines correspond to microscopic and PDE simulations, respectively. Parameters: as in Figs. 1 and 1 except (Lx,Ly)=(8000,600) in panel (a).

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  • Figure 3
    Figure 3

    (a) Potential V(m) entering the Newton mapping with an illustration of the heterocline corresponding to the interface between the droplet and the ordered phase. (b) Speeds of the three interfaces as a function of β. Solid lines correspond to values predicted by the Newton mapping. Symbols are measurements from microscopic simulations with (Lx,Ly)=(3000,300) and ordered phase density ρo=30. Parameters: D=v=1. (c) Comet front profiles aligned at r^=0 from 2D AIM simulations at t=4800 and as predicted by Eq. (11).

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