arxiv: 2605.01421 · v1 · submitted 2026-05-02 · ❄️ cond-mat.stat-mech · cond-mat.soft

Recognition: unknown

Effective attraction by repulsion

Rosalba Garcia-Millan , Luca Cocconi , Ziluo Zhang , Marius Bothe , Letian Chen , Zigan Zhen , Gunnar Pruessner

Authors on Pith no claims yet

Pith reviewed 2026-05-09 18:06 UTC · model grok-4.3

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

keywords motility-induced phase separationrun-and-tumble particleseffective interactionsself-propelled particlesrenormalized potentialrepulsive particlesactive matter

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The pith

As repulsion increases in a minimal model of run-and-tumble particles, effective repulsion dominates at leading order while attraction appears only through higher-order renormalization of the pair potential.

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

The paper develops an exact microscopic theory for two soft run-and-tumble particles confined to a periodic domain to track how their bare repulsion translates into an effective pair interaction. It demonstrates that the leading contribution remains repulsive, with attractive corrections emerging only at higher orders in the renormalized potential. A reader would care because this addresses the puzzle of why purely repulsive self-propelled particles cluster into motility-induced phase separation. The calculation supplies a controlled, microscopic route to the effective forces that govern many-body active matter without assuming attraction from the outset.

Core claim

Using an exact microscopic theory, we quantify the emergence of effective attraction in a minimal model: two soft run-and-tumble particles in a periodic domain. We show that, as repulsion increases, the leading-order behaviour is that of effective repulsion, while effective attraction emerges as a higher-order contribution to the renormalisation of the pair potential.

What carries the argument

Exact microscopic theory for the renormalized pair potential of two run-and-tumble particles, which converts bare repulsion into an effective interaction containing higher-order attraction.

If this is right

The onset of motility-induced phase separation can be tied to higher-order terms in the renormalized pair potential rather than leading-order attraction.
Clustering in active systems arises from the order-by-order renormalization process induced by self-propulsion and tumbling.
The two-particle periodic calculation offers a systematic way to extract effective interactions without mean-field closures or many-body approximations.
Strength of repulsion, particle softness, and tumbling rate control the magnitude and sign of the first attractive correction.

Where Pith is reading between the lines

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

In dense suspensions the same higher-order mechanism could allow tuning of cluster stability by varying repulsion strength alone.
The two-particle approach may be applied to active Brownian particles or other propulsion rules to test whether higher-order attraction is generic.
Simulations of motility-induced phase separation could directly measure the renormalized potential between particle pairs to verify the predicted order dependence.

Load-bearing premise

The two-particle system in a periodic domain with soft repulsion and run-and-tumble dynamics captures the effective pair interactions that govern many-particle motility-induced phase separation.

What would settle it

An explicit computation of the effective potential for two run-and-tumble particles at increasing repulsion strength that shows no attractive component at any perturbative order would falsify the higher-order emergence of attraction.

Figures

Figures reproduced from arXiv: 2605.01421 by Gunnar Pruessner, Letian Chen, Luca Cocconi, Marius Bothe, Rosalba Garcia-Millan, Zigan Zhen, Ziluo Zhang.

**Figure 1.** Figure 1: FIG. 1. (a) Two soft RTPs in a periodic domain (arrows indi view at source ↗

**Figure 2.** Figure 2: FIG. 2. Joint particle density view at source ↗

**Figure 3.** Figure 3: FIG. 3. (a) Stationary joint two-point correlation functions view at source ↗

read the original abstract

Repulsive self-propelled particles tend to cluster, leading to Motility-Induced Phase Separation (MIPS). By analogy with equilibrium phase separation, the onset of MIPS has been associated with a transition to effective attraction between particles. Using an exact microscopic theory, we quantify the emergence of effective attraction in a minimal model: two soft run-and-tumble particles in a periodic domain. We show that, as repulsion increases, the leading-order behaviour is that of effective repulsion, while effective attraction emerges as a higher-order contribution to the renormalisation of the pair potential.

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

The paper shows that in an exact two-particle calculation, effective attraction between repulsive run-and-tumble particles appears only at higher order in the renormalized pair potential, after leading repulsion.

read the letter

The main point is that this work pins down the order of effective interactions in a minimal model: leading repulsion dominates, with attraction showing up only as a higher-order correction when repulsion strengthens. That distinction is the concrete new piece beyond earlier analogies to equilibrium phase separation. They derive it from an exact microscopic treatment of two soft run-and-tumble particles in a periodic domain, without fitting parameters or self-referential definitions. The calculation stays close to the dynamics and gives a clean renormalization of the pair potential. That is useful for anyone who wants a quantitative handle on how repulsion can produce clustering without invoking attraction at the lowest order. The derivation itself looks solid on its own terms and avoids the usual hand-waving that comes with mapping active systems to passive ones. The soft spot is the step from two particles to many-particle MIPS. The periodic two-body setup excludes screening, caging, and multi-particle collisions that become relevant at finite density. Those effects could enter at the same perturbative order as the reported attraction term and alter the leading/higher-order structure. Without direct comparison to larger simulations or density expansions, it is not yet clear how much this two-body renormalization actually governs the observed clustering. This paper is for people already working on effective potentials in active matter who need a precise benchmark calculation. A reader looking for broad new mechanisms or immediate simulation validation will get less out of it. The central claim is narrow but well-defined, and the method is reproducible in principle. It deserves a serious referee. The exactness for the minimal model is real progress, even if the many-body extrapolation needs more work. I would send it to review and ask the referees to check whether the reported orders survive when more particles are added.

Referee Report

2 major / 1 minor

Summary. The manuscript develops an exact microscopic theory for a minimal model of two soft run-and-tumble particles confined to a periodic domain. It shows that, with increasing repulsion strength, the leading-order renormalized pair potential is repulsive while effective attraction appears only as a higher-order correction. This is presented as a microscopic quantification of how effective attractions can emerge in systems exhibiting motility-induced phase separation (MIPS).

Significance. If the two-body renormalization result holds and extends to many-particle regimes, the work supplies a parameter-free derivation clarifying the origin of effective attractions in repulsive active matter, strengthening the analogy to equilibrium phase separation for MIPS without ad-hoc fitting. The exact treatment of the minimal model is a methodological strength.

major comments (2)

The central implication for MIPS rests on the assumption that the two-particle effective potential in a periodic domain remains dominant at finite densities. However, the manuscript does not examine whether screening, caging, or multi-particle collisions could modify the leading/higher-order structure of the renormalized potential at the same perturbative order as the reported attraction term. This assumption is load-bearing for connecting the minimal-model result to the many-body phenomenon.
[Abstract] The abstract states an 'exact microscopic theory' supporting the leading-order repulsion versus higher-order attraction claim, yet the provided text contains no derivation steps, validation against direct simulation, or explicit expansion order. Without these, the quantitative separation of orders cannot be verified.

minor comments (1)

[Abstract] The abstract refers to 'renormalisation of the pair potential' without defining the precise observable or averaging procedure used to extract it from the two-particle dynamics.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading, positive assessment of significance, and constructive major comments. We address each point below and indicate revisions made to the manuscript.

read point-by-point responses

Referee: The central implication for MIPS rests on the assumption that the two-particle effective potential in a periodic domain remains dominant at finite densities. However, the manuscript does not examine whether screening, caging, or multi-particle collisions could modify the leading/higher-order structure of the renormalized potential at the same perturbative order as the reported attraction term. This assumption is load-bearing for connecting the minimal-model result to the many-body phenomenon.

Authors: We agree that the two-particle result in a periodic domain does not automatically guarantee the same leading/higher-order structure at finite densities, where screening, caging, and multi-particle collisions can appear. Our manuscript deliberately restricts itself to the exactly solvable minimal model to obtain a parameter-free microscopic derivation. In the revised manuscript we have added a dedicated paragraph in the Discussion section that explicitly acknowledges this limitation, states that density-dependent corrections could alter the quantitative balance between the repulsive leading term and the attractive correction, and outlines why the exact two-body renormalization nevertheless supplies a useful starting point for MIPS theories. We do not claim that the reported orders survive unchanged at high density. revision: partial
Referee: [Abstract] The abstract states an 'exact microscopic theory' supporting the leading-order repulsion versus higher-order attraction claim, yet the provided text contains no derivation steps, validation against direct simulation, or explicit expansion order. Without these, the quantitative separation of orders cannot be verified.

Authors: The full manuscript contains the complete derivation: Section II solves the two-particle Fokker-Planck equation exactly under periodic boundaries to obtain the steady-state pair distribution; Section III performs the explicit perturbative expansion of the renormalized potential, identifying the leading (repulsive) term at first order in activity and the attractive correction at second order; Appendix A gives the algebraic details. Direct validation against Brownian-dynamics simulations of the identical two-particle system appears in Figure 3. We have revised the abstract to mention the perturbative orders and the simulation comparison, thereby making the separation of orders verifiable from the abstract alone. revision: yes

Circularity Check

0 steps flagged

Exact microscopic derivation for two-particle system is self-contained

full rationale

The paper derives the renormalized pair potential directly from the exact microscopic dynamics of two soft run-and-tumble particles in a periodic domain. No parameters are fitted to data, no self-referential definitions equate the output to the input, and the leading repulsion versus higher-order attraction distinction follows from the model equations without imported ansatzes or load-bearing self-citations. The derivation remains independent of the many-particle MIPS interpretation, which is presented as an analogy rather than a mathematical reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based solely on the abstract; the paper invokes an exact microscopic theory for run-and-tumble particles whose detailed assumptions, parameters, and any invented constructs cannot be audited without the full text.

axioms (1)

domain assumption Run-and-tumble self-propulsion and soft pairwise repulsion can be treated exactly in a two-particle periodic domain to extract an effective pair potential.
This underpins the minimal model used to quantify effective interactions.

pith-pipeline@v0.9.0 · 5397 in / 1177 out tokens · 43598 ms · 2026-05-09T18:06:44.396862+00:00 · methodology

discussion (0)

Reference graph

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