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arxiv: 2606.27310 · v1 · pith:5K7CLAAYnew · submitted 2026-06-25 · ❄️ cond-mat.stat-mech · cond-mat.soft

Proactivity and pinning in the non-reciprocal XY model with vision anisotropy

Gabriele Bandini , Asja Jelic , Andrea Gambassi This is my paper

Pith reviewed 2026-06-26 02:08 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech cond-mat.soft
keywords non-reciprocal XY modelvision anisotropydirectional pinningLangevin dynamicsreactive and proactive termslattice orientation selectionstatistical mechanics
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The pith

In the non-reciprocal XY model with vision anisotropy, both reactive and proactive terms in the Langevin dynamics produce global pinning of spin orientation to lattice directions.

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

This paper examines a non-reciprocal XY model on a square lattice where nearest-neighbor interactions depend on anisotropic vision kernels that break rotational symmetry. The resulting directional pinning of spin orientations is analyzed for several kernels and for both Glauber and Langevin microscopic dynamics. The authors separate the Langevin drift into two contributions, called reactive and proactive, and derive the equations they obey for local fluctuations and for the global orientation. They demonstrate that both contributions can drive global pinning while the details of local pinning depend on the kernel shape, thereby explaining preferred lattice directions and reconciling earlier observations.

Core claim

The central claim is that the Langevin formulation naturally separates the interaction into reactive and proactive terms; both terms generate global pinning of the overall spin orientation, whereas their respective roles in local pinning vary qualitatively with the choice of vision kernel such as modulated, sinusoidal, von Mises, or hard-cone forms.

What carries the argument

The decomposition of the Langevin drift into reactive and proactive terms, which separately govern the dynamics of local fluctuations and the global orientation to produce directional pinning.

If this is right

  • Both reactive and proactive contributions generate global pinning for modulated, sinusoidal, von Mises, and hard-cone kernels.
  • The contribution of each term to local pinning differs qualitatively depending on the specific interaction kernel.
  • The framework distinguishes local from global pinning and accounts for the emergence of preferred lattice directions under non-reciprocal interactions.
  • The same separation applies under both Glauber and Langevin microscopic update rules.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same term separation could be applied to non-reciprocal models on other lattices to test whether pinning remains tied to square symmetry.
  • The proactive term may connect to anticipatory mechanisms in related active-matter systems with broken reciprocity.
  • Numerical checks with continuous-time versus discrete-time updates could reveal whether the clean separation holds beyond the rules examined here.

Load-bearing premise

The interaction term in the Langevin equation can be cleanly separated into reactive and proactive contributions that remain distinct and physically meaningful for the family of vision kernels and update rules considered.

What would settle it

A simulation in which one of the two terms is removed from the Langevin equation and global pinning to lattice directions disappears would show that both terms are required for the reported effect.

Figures

Figures reproduced from arXiv: 2606.27310 by Andrea Gambassi, Asja Jelic, Gabriele Bandini.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Pinning coefficients for the modulated [PITH_FULL_IMAGE:figures/full_fig_p019_6.png] view at source ↗
read the original abstract

We study a non-reciprocal XY model on a square lattice, in which spins interact with their nearest neighbors through vision-induced anisotropic interaction. Such anisotropy breaks rotational symmetry and leads to the pinning of the spin orientation along preferred lattice directions. We systematically characterize this phenomenon for different interaction kernels, including modulated, sinusoidal, von Mises, and hard vision-cone couplings, and for two classes of microscopic update rules: Glauber and Langevin dynamics. A central result of this work is the identification and detailed analysis of two distinct contributions that naturally arise in the Langevin formulation, which we refer to as the reactive and the proactive term. We derive the corresponding equations governing both local fluctuations and the global orientation, and use them to characterize the mechanisms responsible for directional pinning. We show that both reactive and proactive contributions can generate global pinning, whereas their role in determining local pinning depends on the specific interaction kernel and may differ qualitatively. Our analysis clarifies the distinction between local and global pinning, explains the emergence of preferred lattice directions in the different models considered, and reconciles apparent discrepancies reported in previous studies. More generally, it provides a microscopic framework for understanding lattice-induced orientational selection in non-reciprocal XY models.

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.

Referee Report

1 major / 1 minor

Summary. The manuscript studies a non-reciprocal XY model on a square lattice with vision-induced anisotropic interactions that break rotational symmetry and produce directional pinning. It examines four interaction kernels (modulated, sinusoidal, von Mises, hard vision-cone) under Glauber and Langevin dynamics, identifies reactive and proactive terms that arise in the Langevin formulation, derives equations for local fluctuations and global orientation, and shows that both terms can generate global pinning while their roles in local pinning depend on the kernel.

Significance. If the derivations are valid, the work supplies a microscopic decomposition that distinguishes local from global pinning mechanisms and reconciles apparent discrepancies across prior studies of lattice-induced orientational selection in non-reciprocal XY models. The explicit tracking of separate contributions to the drift is a clear strength.

major comments (1)
  1. [Langevin formulation and decomposition] Langevin formulation section: the claim that the interaction drift cleanly separates into reactive and proactive terms whose effects on pinning can be tracked independently is load-bearing for the central results. For the hard vision-cone and von Mises kernels the microscopic update produces a non-analytic truncation; the continuous-time limit therefore requires an explicit Itô–Stratonovich convention, and the manuscript must demonstrate that cross terms do not mix reactive components into the proactive equation (or vice versa).
minor comments (1)
  1. Figure captions and equation numbering should be checked for consistency when referring to the four kernels; a short table summarizing which term dominates local versus global pinning for each kernel would improve readability.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and for highlighting a key technical point regarding the Langevin formulation. We address the concern below and commit to revisions that strengthen the presentation of the reactive/proactive decomposition.

read point-by-point responses

  1. Referee: Langevin formulation section: the claim that the interaction drift cleanly separates into reactive and proactive terms whose effects on pinning can be tracked independently is load-bearing for the central results. For the hard vision-cone and von Mises kernels the microscopic update produces a non-analytic truncation; the continuous-time limit therefore requires an explicit Itô–Stratonovich convention, and the manuscript must demonstrate that cross terms do not mix reactive components into the proactive equation (or vice versa).

    Authors: We agree that an explicit statement of the stochastic calculus convention is necessary for the non-analytic kernels. In the revised manuscript we will add a dedicated subsection (or appendix) that (i) specifies the Itô interpretation adopted for the continuous-time limit of the hard vision-cone and von Mises updates, (ii) derives the drift terms under that convention, and (iii) explicitly verifies that the reactive and proactive contributions remain orthogonal—no cross terms appear in the respective equations of motion. This demonstration will be performed both analytically for the sinusoidal and modulated kernels and numerically for the non-analytic cases, confirming that the separation used in the main text is preserved. The main conclusions are unaffected, but the added material removes any ambiguity. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivations follow from model definitions

full rationale

The paper's central claims rest on explicit derivations of reactive and proactive terms from the Langevin equation applied to the defined non-reciprocal XY model with various vision kernels (modulated, sinusoidal, von Mises, hard cone) under Glauber and Langevin dynamics. These terms are stated to 'naturally arise' in the formulation, and the subsequent equations for local fluctuations and global orientation are obtained directly from the microscopic rules without fitting parameters to the pinning phenomenon or reducing the decomposition to prior self-citations. No load-bearing step equates a prediction to its input by construction, imports uniqueness via self-citation, or renames a known result; the analysis of directional pinning is therefore self-contained and independent of the target observations.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The paper introduces the proactive term as a distinct dynamical contribution arising from the non-reciprocal vision kernel; its separation from the reactive term is an additional modeling step not required by standard Langevin dynamics. No explicit free parameters are named in the abstract, but the shape parameters of each kernel (modulation amplitude, concentration parameter, cone angle) function as model choices that control the pinning phenomenology.

axioms (1)
  • domain assumption The microscopic dynamics (Glauber or Langevin) are Markovian and the interaction is strictly nearest-neighbor on the square lattice.
    Standard assumption for lattice spin models; invoked when the authors define the update rules and interaction kernels.
invented entities (1)
  • proactive term no independent evidence
    purpose: Captures the component of the Langevin drift that depends on the anticipated change in neighbor orientations due to the non-reciprocal vision kernel.
    Introduced in the abstract as one of the two distinct contributions whose separate analysis explains global and local pinning.

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    Modulated coupling We consider the reactive (first line) and the proactive (second line) contributions together, and obtain ∂tϕ=− ϵ N X ⟨i,j⟩ cos(4(ϕ+δ ˜ϕi))−cos(4(ϕ+δ ˜ϕj)) sin(δ ˜ϕi −δ ˜ϕj) − 4ϵ N X ⟨i,j⟩ sin(4(ϕ+δ ˜ϕi)) + sin(4(ϕ+δ ˜ϕj)) cos(δ ˜ϕi −δ ˜ϕj), (B1) where we expressed the local valueϕ i of the phase in terms of its deviationδ ˜ϕi from the g...

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    Sinusoidal coupling For the case of the sinusoidal coupling in Eq. (5), we find convenient to treat separately the reactive and proactive contributions to the equation of motion in Eq. (3), which we then use to determine the equation of motion for the average orientationϕ(t), as done above. Reactive term.The deterministic contribution to the Langevin dyna...

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    V on Mises coupling As done above, also for the case of the von Mises coupling in Eq. (6), we find convenient to treat separately the reactive and proactive contributions to the equation of motion in Eq. (3), which we then use to determine the equation of motion for the average orientationϕ(t). In particular, we consider the ordersO(σ) andO(σ 4) of the ex...