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Stability of discrete-symmetry flocks: Sandwich state, traveling domains, and motility-induced pinning

Swarnajit Chatterjee1,2,*,†, Mintu Karmakar3,4,5,6,*,‡, Matthieu Mangeat1,§, Heiko Rieger1,∥, and Raja Paul3,#

  • *These authors contributed equally to this work.
  • †Contact author: swarnajit.chatterjee@cyu.fr
  • ‡Contact author: mkarmakar094@ucas.ac.cn
  • §Contact author: mangeat@lusi.uni-sb.de
  • ∥Contact author: heiko.rieger@uni-saarland.de
  • #Contact author: raja.paul@iacs.res.in
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Phys. Rev. E 112, 064115 – Published 11 December, 2025

DOI: https://doi.org/10.1103/1r19-ryx9

Abstract

Polar flocks in discrete active systems are often assumed to be robust, yet recent studies reveal their fragility under both imposed and spontaneous fluctuations. Here, we revisit the four-state active Potts model and show that its globally ordered phase is metastable across a broad swath of parameter space. Small counterpropagating droplets disrupt the flocking phase by inducing a persistent sandwich state, where the droplet-induced opposite-polarity lane remains embedded within the original flock, particularly pronounced at low noise, influenced by spatial anisotropy. In contrast, small transversely propagating droplets, when introduced into the flock, can trigger complete phase reversal due to their alignment orthogonal to the dominant flow and their enhanced persistence. At low diffusion and strong self-propulsion, such transverse droplets also emerge spontaneously, fragmenting the flock into multiple traveling domains and giving rise to a short-range order (SRO) regime. We further identify a motility-induced pinning (MIP) transition in small diffusion and low-temperature regimes when particles of opposite polarity interact, flip their state, hop, and pin an interface. Our comprehensive phase diagrams, encompassing full reversal, sandwich coexistence, stripe bands, SRO, and MIP, delineate how thermal fluctuations, self-propulsion strength, and diffusion govern flock stability in discrete active matter systems.

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Phys. Rev. E 112, 064115– Published 11 December, 2025
  • Received 10 July 2025
  • Accepted 18 November 2025
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