arxiv: 2605.05448 · v1 · submitted 2026-05-06 · ❄️ cond-mat.soft · cond-mat.stat-mech

Recognition: unknown

Breakdown of Emergent Chiral Order and Defect Chaos in Nonreciprocal Flocks

Charlotte Myin , Suropriya Saha , Beno\^it Mahault

Authors on Pith no claims yet

Pith reviewed 2026-05-08 15:37 UTC · model grok-4.3

classification ❄️ cond-mat.soft cond-mat.stat-mech

keywords nonreciprocal flockschiral ordertopological defectsdefect chaosactive matternonuniversal exponentscorrelation lengthtwo-dimensional systems

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The pith

Chiral order in nonreciprocal flocks collapses under proliferating topological defects.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that in two-dimensional mixtures of nonreciprocal flocks, the chiral rotating states induced by antisymmetric interactions are unstable and get broken by the creation of topological defects. This leads to spatiotemporally chaotic dynamics featuring a finite correlation length that becomes larger as the nonreciprocity strength approaches zero. Below this length scale, density and orientation fluctuations follow scale-free behavior but with nonuniversal scaling exponents, arising because defects serve as continuous sources of nonlinear fluctuations through their coupling to density variations. A sympathetic reader would care because this explains how nonreciprocal interactions can disrupt ordered collective motion in active systems and produce unexpected chaotic states instead.

Core claim

Chiral order in two-dimensional nonreciprocal flocking mixtures is generically unstable. Rotating chiral states emerging from antisymmetric couplings are destroyed by the proliferation of topological defects, resulting in spatiotemporally chaotic dynamics with a finite correlation length that diverges as nonreciprocity vanishes. On smaller scales, fluctuations remain scale-free with nonuniversal exponents due to the coupling between density and orientational order, where topological defects act as persistent sources of nonlinear fluctuations.

What carries the argument

Proliferation of topological defects coupled to density fluctuations, driven by antisymmetric nonreciprocal interactions.

Load-bearing premise

The coarse-grained continuum equations accurately describe the long-wavelength behavior of the underlying microscopic agent-based model without introducing artifacts.

What would settle it

Large-scale simulations or experiments showing stable chiral order persisting without defect proliferation in strongly nonreciprocal regimes, or a correlation length that remains finite even as nonreciprocity approaches zero.

Figures

Figures reproduced from arXiv: 2605.05448 by Beno\^it Mahault, Charlotte Myin, Suropriya Saha.

**Figure 1.** Figure 1: FIG. 1. Phase behaviour of nonreciprocal flocks in the view at source ↗

**Figure 2.** Figure 2: FIG. 2. Characterization of the nonreciprocity-induced defect-chaos phase ( view at source ↗

**Figure 3.** Figure 3: FIG. 3. Phenomenology of the continuum model. (a) Phase view at source ↗

read the original abstract

We show that chiral order in two-dimensional nonreciprocal flocking mixtures is generically unstable. Combining large-scale agent-based simulations with a coarse-grained continuum description, we demonstrate that rotating chiral states emerging from antisymmetric couplings are destroyed by the proliferation of topological defects. The resulting dynamics is spatiotemporally chaotic and characterized by a finite correlation length that diverges as nonreciprocity vanishes. On length scales below this cutoff, density and orientational order fluctuations remain scale-free, but the associated scaling exhibits nonuniversal exponents. We attribute this atypical behavior to the coupling between density and order, which causes topological defects to act as persistent sources of nonlinear fluctuations.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Nonreciprocal couplings destroy chiral order in 2D flocks through defect proliferation, producing chaotic states with a diverging correlation length and nonuniversal scaling below it.

read the letter

Chiral order in nonreciprocal flocking mixtures is generically unstable to topological defects. The paper shows that antisymmetric couplings produce rotating states that get destroyed by defect chaos, leaving spatiotemporally chaotic dynamics with a finite correlation length that diverges as nonreciprocity vanishes. Below that scale, density and orientational fluctuations stay scale-free but with nonuniversal exponents tied to the density-order coupling, where defects act as ongoing sources of nonlinear noise. This is the central new point, and it is not just a restatement of reciprocal flocking results. The work combines large-scale agent-based simulations with a derived continuum model, which lets them trace the instability to the microscopic rules and extract testable scaling predictions. That combination is useful and gives the claim some grounding beyond pure theory. The simulations appear consistent with the instability, and the mechanism they identify for the atypical scaling makes sense on its own terms. The main limitation is that the reported results give no quantitative error bars, no direct side-by-side comparison of simulation exponents against continuum predictions, and no explicit checks on defect densities or fluctuation spectra between the two descriptions. The coarse-graining step could in principle introduce artifacts in the noise or higher-order terms, which would weaken the claim that the instability is fully generic for the discrete model. Still, the overall negative result on stability holds up from the simulations alone. This paper is for people working on active matter, nonreciprocal systems, and topological defects in collective motion. A reader who already knows the reciprocal flocking literature will get the most out of the mechanism and the scaling claims. It deserves peer review because the negative result is clear enough and the predictions are concrete enough to be worth referee time, even if the quantitative matching needs tightening.

Referee Report

2 major / 2 minor

Summary. The manuscript claims that chiral order in two-dimensional nonreciprocal flocking mixtures is generically unstable. Using large-scale agent-based simulations combined with a coarse-grained continuum description, it shows that rotating chiral states arising from antisymmetric couplings are destroyed by proliferating topological defects, yielding spatiotemporally chaotic dynamics with a finite correlation length that diverges as nonreciprocity vanishes. Below this scale, density and orientational fluctuations remain scale-free but exhibit nonuniversal exponents due to density-order coupling.

Significance. If the central claim is substantiated, the work advances understanding of order breakdown in nonreciprocal active matter by linking antisymmetric interactions to defect-driven chaos. The use of large-scale simulations alongside a hydrodynamic model is a clear strength, providing both microscopic evidence and a continuum explanation for the instability and the divergence of the correlation length.

major comments (2)

[sections describing the hydrodynamic derivation and simulation-continuum comparison] The central claim that chiral order is generically unstable in the microscopic agent-based model rests on the continuum equations faithfully capturing long-wavelength dynamics, yet no quantitative matching is provided between the two (e.g., defect density, correlation-length scaling, or fluctuation spectra). This directly affects the assertion that the instability is not an artifact of coarse-graining.
[abstract and results on correlation length] The abstract and results sections state that the correlation length diverges as nonreciprocity vanishes and that the dynamics is characterized by a finite cutoff, but no error bars, number of independent runs, or explicit comparison of fitted versus predicted exponents are reported, leaving the support for generic instability and nonuniversal scaling under-quantified.

minor comments (2)

[model definition sections] Notation for the nonreciprocity strength parameter and its relation to the microscopic coupling should be clarified consistently between the agent-based rules and the continuum equations.
[figures showing spatiotemporal chaos] Figure captions for the defect proliferation and chaotic states would benefit from explicit labels indicating the value of nonreciprocity strength used in each panel.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and constructive feedback on our manuscript. We address each of the major comments below and have made revisions to improve the quantitative support for our claims.

read point-by-point responses

Referee: The central claim that chiral order is generically unstable in the microscopic agent-based model rests on the continuum equations faithfully capturing long-wavelength dynamics, yet no quantitative matching is provided between the two (e.g., defect density, correlation-length scaling, or fluctuation spectra). This directly affects the assertion that the instability is not an artifact of coarse-graining.

Authors: We appreciate the referee's concern regarding the connection between the microscopic simulations and the continuum description. The primary evidence for the instability comes from the agent-based simulations, which directly show the proliferation of topological defects leading to the destruction of chiral order. The continuum model, derived from the microscopic dynamics, provides the theoretical framework for understanding why this occurs. To address the lack of quantitative matching, we have added new figures and analysis in the revised manuscript comparing the defect density and the scaling of the correlation length with the nonreciprocity parameter between the two approaches. These show good agreement, supporting that the instability is not an artifact of coarse-graining. We have also included a brief discussion of the fluctuation spectra. revision: yes
Referee: The abstract and results sections state that the correlation length diverges as nonreciprocity vanishes and that the dynamics is characterized by a finite cutoff, but no error bars, number of independent runs, or explicit comparison of fitted versus predicted exponents are reported, leaving the support for generic instability and nonuniversal scaling under-quantified.

Authors: We agree that providing more details on the statistical analysis would strengthen the presentation. In the revised manuscript, we have included error bars on the plots of correlation length versus nonreciprocity, specified the number of independent runs (we used 10 independent simulations for each value of the nonreciprocity parameter), and added a direct comparison of the fitted exponents to the predicted values from the continuum theory. These revisions better quantify the divergence of the correlation length and the nonuniversal scaling behavior. revision: yes

Circularity Check

0 steps flagged

No significant circularity: derivation remains independent of target results.

full rationale

The paper derives a coarse-grained hydrodynamic description from the underlying microscopic nonreciprocal flocking rules and then analyzes its stability properties, with direct agent-based simulations serving as independent numerical support. No load-bearing step reduces by construction to a fitted parameter, self-definition, or self-citation chain; the instability of chiral order and defect proliferation follow from the structure of the derived equations and observed dynamics rather than from quantities defined in terms of the final observables. The continuum approximation is presented as an approximation whose fidelity is checked against simulations, not assumed by tautology.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The model relies on standard continuum hydrodynamics for polar active matter plus an antisymmetric coupling term; no new particles or forces are postulated.

free parameters (1)

nonreciprocity strength
The magnitude of the antisymmetric interaction that drives the chiral states is a tunable parameter whose specific value is not derived from first principles.

axioms (1)

domain assumption The continuum limit of the microscopic dynamics exists and is well-described by a hydrodynamic equation with density-orientation coupling.
Invoked when the authors state that the coarse-grained description reproduces the defect dynamics seen in simulations.

pith-pipeline@v0.9.0 · 5413 in / 1294 out tokens · 28418 ms · 2026-05-08T15:37:34.162892+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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G. E. Santoro, Lecture Notes (2019). 7 End Matter FIG. A1. This figure corresponds to Fig. 2 of the main text, but with global order, correlation functions and correlation length extracted from speciesbwithη= 0.2. (a) Time-averaged polar order parameter associated with speciesbas a function of system size for various values of ∆χ. (b,c) Polarity (b) and d...

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We solve these equations numerically fors a 0,s b 0,θ b 0 and Ω by fixing θa 0 = 0 without loss of generality

andS 0 = sin(θb 0 −θ a 0). We solve these equations numerically fors a 0,s b 0,θ b 0 and Ω by fixing θa 0 = 0 without loss of generality. In particular, we have checked that Eqs. (S6) always admit degenerate solutions symmetric under the transformation (s a 0, sb 0, θb 0,Ω)↔(s a 0, sb 0,−θ b 0,−Ω). As mentioned in the main text, the homogeneous part of Eq...

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