arxiv: 2605.13561 · v1 · submitted 2026-05-13 · ❄️ cond-mat.soft · cond-mat.stat-mech

Recognition: 1 theorem link

· Lean Theorem

Metastable Hyperuniformity at Discontinuous Absorbing Transitions

Yusheng Lei , Ran Ni

Authors on Pith no claims yet

Pith reviewed 2026-05-14 17:56 UTC · model grok-4.3

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

keywords hyperuniformityabsorbing state transitionsmetastable regimeconserved densityManna modelReggeon field theorydemographic noiseactive matter

0 comments

The pith

Discontinuous absorbing transitions generically host a metastable hyperuniform regime near their stability limit.

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

The paper establishes that discontinuous absorbing transitions in nonequilibrium systems with conserved density exhibit a metastable hyperuniform regime close to the point where the active phase loses stability. In this regime, density fluctuations follow an anomalous scaling where the structure factor S(k) behaves as k to the power 1.2 near zero wavevector. This behavior is observed using the facilitated Manna model and reproduced by a minimal conserved Reggeon field theory. It arises specifically from the combination of nonlinear activation, multiplicative noise, and diffusive conservation laws, appearing only near the transition and vanishing in both the active and absorbing phases. The finding suggests a new pseudo-critical signature distinct from hyperuniformity at continuous transitions.

Core claim

Discontinuous absorbing transitions generically host a metastable hyperuniform regime near the stability limit. Using a facilitated Manna model without center-of-mass conservation, anomalous scaling S(k→0)∼k^{1.2} is found, which appears only near the metastable regime and disappears both deep in the active phase and in the absorbing phase. This scaling is robust in both two and three dimensions. A minimal conserved Reggeon field theory reproduces the same regime, showing that the phenomenon arises from the interplay of nonlinear activation, multiplicative demographic noise, and conserved diffusive fluctuations.

What carries the argument

The metastable hyperuniform regime, arising from the interplay of nonlinear activation, multiplicative demographic noise, and conserved diffusive fluctuations in systems undergoing discontinuous absorbing transitions coupled to conserved density.

If this is right

The anomalous scaling is robust in two and three dimensions, unlike critical hyperuniformity at continuous transitions.
The scaling appears only near the metastable regime and is absent deep in the active or absorbing phases.
The phenomenon does not depend on specific microscopic details but emerges generically from the field-theoretic ingredients.
Metastable hyperuniformity serves as a pseudo-critical structural signature for such transitions.

Where Pith is reading between the lines

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

Experimental systems with conserved particle number, such as colloidal suspensions or biological populations, might display similar scaling near their transition points.
Measuring the structure factor at small k could provide a practical way to locate the stability limit in driven systems.
This suggests that hyperuniformity can be a transient or metastable feature rather than only a steady-state or critical one.
Extensions to higher dimensions or other noise types could test the universality of the 1.2 exponent.

Load-bearing premise

The facilitated Manna model without center-of-mass conservation and the minimal conserved Reggeon field theory capture the generic behavior of all discontinuous absorbing transitions coupled to conserved density.

What would settle it

A direct numerical test showing whether the structure factor scaling S(k→0) ∼ k^{1.2} persists in other models of discontinuous absorbing transitions or disappears when center-of-mass conservation is restored in the Manna model.

Figures

Figures reproduced from arXiv: 2605.13561 by Ran Ni, Yusheng Lei.

**Figure 1.** Figure 1: FIG. 1: Facilitated Manna model in 2D. (A) Schematic diagram of the facilitated Manna model. Red and grey colors represent [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗

**Figure 2.** Figure 2: FIG. 2: Reggeon field theory simulation in 2D with system [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3: Comparison between Facilitated Manna model and the Reggeon field theory simulation in 3D. (A) Facilitated Manna [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

read the original abstract

Nonequilibrium hyperuniformity can arise either as a steady-state property of driven active fluids or as a critical signature at continuous absorbing transition points in two and three dimensions. Whether analogous structural order exists near discontinuous absorbing transitions, and what mechanism generates it, remains unclear. Here, we show that discontinuous absorbing transitions generically host a metastable hyperuniform regime near the stability limit. Using a facilitated Manna model without center-of-mass conservation, we find anomalous scaling $S(k\to0)\sim k^{1.2}$, which appears only near the metastable regime and disappears both deep in the active phase and in the absorbing phase. This scaling is robust in both two and three dimensions, in contrast to critical hyperuniformity at continuous absorbing transitions. We further formulate a minimal conserved Reggeon field theory that reproduces the same metastable hyperuniform regime and anomalous scaling, demonstrating that the phenomenon does not rely on microscopic update rules but arises from the interplay of nonlinear activation, multiplicative demographic noise, and conserved diffusive fluctuations. These results identify metastable hyperuniformity as a generic pseudo-critical structural signature of discontinuous absorbing transitions coupled to a conserved density.

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 reports metastable hyperuniformity with S(k) ~ k^{1.2} near discontinuous absorbing transitions in one model and a matching field theory, but the generic claim rests on limited cross-checks.

read the letter

The main thing to know is that this paper identifies a metastable hyperuniform regime near discontinuous absorbing transitions, with anomalous scaling S(k to 0) ~ k to the 1.2 that appears only close to the stability limit. They see it in lattice simulations of the facilitated Manna model without center-of-mass conservation, and it vanishes both deep in the active phase and in the absorbing phase. The scaling holds in two and three dimensions. They then build a minimal conserved Reggeon field theory that reproduces the same regime and scaling, tracing it to nonlinear activation, multiplicative noise, and conserved diffusion rather than microscopic details. This is new relative to earlier work that focused on continuous transitions. The simulation-theory match is a strength, and the field theory is built from standard ingredients without obvious parameter fitting, which keeps circularity low. The main soft spot is the genericity. The headline states that discontinuous absorbing transitions generically host this regime, yet the evidence is from a single lattice model and one minimal field theory. There are no tests on other realizations such as different facilitation thresholds or off-lattice variants, so if the 1.2 exponent is tied to the specific nonlinear terms shared by these two setups, the broader claim does not follow yet. The abstract also omits system sizes, statistics, and error bars, which makes the numerical support harder to assess. This work is for researchers in nonequilibrium statistical mechanics and soft matter who study absorbing states or hyperuniformity in driven systems. A reader interested in structural signatures of phase transitions would find the new regime useful. It deserves peer review because the combination of concrete simulation results and a reproducing field theory is solid enough to warrant referee time, even if the authors need to address the scope of the genericity claim.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on numerical observations in one specific lattice model and a minimal phenomenological field theory built to reproduce those observations; no explicit free parameters are introduced beyond standard model definitions, and no new entities are postulated.

axioms (1)

domain assumption The facilitated Manna model without center-of-mass conservation is representative of generic discontinuous absorbing transitions coupled to conserved density
Invoked as the primary numerical platform whose results are then generalized via the field theory.

pith-pipeline@v0.9.0 · 5491 in / 1378 out tokens · 45691 ms · 2026-05-14T17:56:26.521024+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

anomalous scaling S(k→0)∼k^{1.2}... arises from the interplay of nonlinear activation, multiplicative demographic noise, and conserved diffusive fluctuations

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

50 extracted references · 50 canonical work pages

[1]

Torquato and F

S. Torquato and F. H. Stillinger, Phys. Rev. E68, 041113 (2003)

work page 2003
[2]

Torquato, Phys

S. Torquato, Phys. Rev. E94, 022122 (2016)

work page 2016
[3]

Torquato, Phys

S. Torquato, Phys. Rep.745, 1 (2018)

work page 2018
[4]

Donev, F

A. Donev, F. H. Stillinger, and S. Torquato, Phys. Rev. Lett.95, 090604 (2005)

work page 2005
[5]

Y. Jiao, T. Lau, H. Hatzikirou, M. Meyer-Hermann, J. C. Corbo, and S. Torquato, Phys. Rev. E89, 022721 (2014)

work page 2014
[6]

Y. Liu, D. Chen, J. Tian, W. Xu, and Y. Jiao, Phys. Rev. Lett.133, 028401 (2024)

work page 2024
[7]

W. Hu, L. Cui, M. Delgado-Baquerizo, R. Sol´ e, S. K´ efi, M. Berdugo, N. Xu, B. Wang, Q.-X. Liu, and C. Xu, Proc. Natl. Acad. Sci. U.S.A.122, e2504496122 (2025)

work page 2025
[8]

Florescu, S

M. Florescu, S. Torquato, and P. J. Steinhardt, Proc. Natl. Acad. Sci. USA106, 20658 (2009)

work page 2009
[9]

W. Man, M. Florescu, E. P. Williamson, Y. He, S. R. Hashemizad, B. Y. Leung, D. R. Liner, S. Torquato, P. M. Chaikin, and P. J. Steinhardt, Proc. Natl. Acad. Sci. USA110, 15886 (2013)

work page 2013
[10]

Lei and R

Y. Lei and R. Ni, J. Phys. Condens. Matter37, 023004 (2025)

work page 2025
[11]

Hexner and D

D. Hexner and D. Levine, Phys. Rev. Lett.118, 020601 (2017)

work page 2017
[12]

Q.-L. Lei, M. P. Ciamarra, and R. Ni, Sci. Adv.5, eaau7423 (2019)

work page 2019
[13]

Lei and R

Q.-L. Lei and R. Ni, Proc. Natl. Acad. Sci. U.S.A.116, 22983 (2019)

work page 2019
[14]

Li, Q.-L

Z.-Q. Li, Q.-L. Lei, and Y.-Q. Ma, Proc. Natl. Acad. Sci. U.S.A.122, e2421518122 (2025)

work page 2025
[15]

Mitra, A

S. Mitra, A. D. Parmar, P. Leishangthem, S. Sastry, and G. Foffi, J. Stat. Mech.: Theory Exp.2021, 033203 (2021)

work page 2021
[16]

Zheng, M

Y. Zheng, M. A. Klatt, and H. L¨ owen, Phys. Rev. Res. 6, L032056 (2024)

work page 2024
[17]

Wilken, A

S. Wilken, A. Chaderjian, and O. A. Saleh, Phys. Rev. X13, 031014 (2023)

work page 2023
[18]

Huang, W

M. Huang, W. Hu, S. Yang, Q.-X. Liu, and H. Zhang, Proc. Natl. Acad. Sci. U.S.A.118, e2100493118 (2021)

work page 2021
[19]

Oppenheimer, D

N. Oppenheimer, D. B. Stein, M. Y. B. Zion, and M. J. Shelley, Nat. Commun.13, 804 (2022)

work page 2022
[20]

Zhang and A

B. Zhang and A. Snezhko, Phys. Rev. Lett.128, 218002 (2022)

work page 2022
[21]

J. H. Weijs, R. Jeanneret, R. Dreyfus, and D. Bartolo, Phys. Rev. Lett.115, 108301 (2015)

work page 2015
[22]

A. Z. Guo, S. Wilken, D. Levine, and P. M. Chaikin, Phys. Rev. E113, 044108 (2026)

work page 2026
[23]

Hexner and D

D. Hexner and D. Levine, Phys. Rev. Lett.114, 110602 (2015)

work page 2015
[24]

Corte, P

L. Corte, P. M. Chaikin, J. P. Gollub, and D. J. Pine, Nat. Phys.4, 420 (2008)

work page 2008
[25]

De Luca, X

F. De Luca, X. Ma, C. Nardini, and M. E. Cates, J. Phys. Condens. Matter36, 405101 (2024)

work page 2024
[26]

Anand, G

S. Anand, G. Zhang, and S. Martiniani, Nat. Commun. 17, 2346 (2026)

work page 2026
[27]

Backofen, A

R. Backofen, A. Y. Altawil, M. Salvalaglio, and A. Voigt, Proc. Natl. Acad. Sci. U.S.A.121, e2320719121 (2024)

work page 2024
[28]

R. L. Jack, I. R. Thompson, and P. Sollich, Phys. Rev. Lett.114, 060601 (2015)

work page 2015
[29]

J. Wang, Z. Sun, H. Chen, G. Wang, D. Chen, G. Chen, J. Shuai, M. Yang, Y. Jiao, and L. Liu, Phys. Rev. Lett. 134, 248301 (2025)

work page 2025
[30]

J. Wang, J. M. Schwarz, and J. D. Paulsen, Nat. Com- mun.9, 2836 (2018). 6

work page 2018
[31]

Maire and L

R. Maire and L. Chaix, J. Chem. Phys.163(2025)

work page 2025
[32]

Kuroda and K

Y. Kuroda and K. Miyazaki, J. Stat. Mech.: Theory Exp. 2023, 103203 (2023)

work page 2023
[33]

Y. Lei, N. Zheng, and R. Ni, J. Chem. Phys.157, 081101 (2023)

work page 2023
[34]

K. J. Wiese, Phys. Rev. Lett.133, 067103 (2024)

work page 2024
[35]

Wilken, R

S. Wilken, R. E. Guerra, D. J. Pine, and P. M. Chaikin, Phys. Rev. Lett.125, 148001 (2020)

work page 2020
[36]

J. Chen, X. Lei, Y. Xiang, M. Duan, X. Peng, and H. Zhang, Phys. Rev. Lett.132, 118301 (2024)

work page 2024
[37]

Tjhung and L

E. Tjhung and L. Berthier, Phys. Rev. Lett.114, 148301 (2015)

work page 2015
[38]

Wilken, R

S. Wilken, R. E. Guerra, D. Levine, and P. M. Chaikin, Phys. Rev. Lett.127, 038002 (2021)

work page 2021
[39]

Galliano, M

L. Galliano, M. E. Cates, and L. Berthier, Phys. Rev. Lett.131, 047101 (2023)

work page 2023
[40]

Ma and S

Z. Ma and S. Torquato, Phys. Rev. E99, 022115 (2019)

work page 2019
[41]

Q.-L. Lei, H. Hu, and R. Ni, Phys. Rev. E103, 052607 (2021)

work page 2021
[42]

Lei and R

Y. Lei and R. Ni, Proc. Natl. Acad. Sci. U.S.A.120, e2312866120 (2023)

work page 2023
[43]

Maire, A

R. Maire, A. Plati, F. Smallenburg, and G. Foffi, J. Stat. Mech. Theory Exp.2025, 123206 (2025)

work page 2025
[44]

Hinrichsen, Adv

H. Hinrichsen, Adv. Phys.49, 815 (2000)

work page 2000
[45]

Di Santo, R

S. Di Santo, R. Burioni, A. Vezzani, and M. A. Mu˜ noz, Physi. Rev. Lett.116, 240601 (2016)

work page 2016
[46]

Janssen and O

H.-K. Janssen and O. Stenull, Phys. Rev. E94, 042138 (2016)

work page 2016
[47]

X. Ma, J. Pausch, G. Pruessner, and M. E. Cates, arXiv preprint arXiv:2507.07793 (2025)

work page arXiv 2025
[48]

K. J. Wiese, Phys. Rev. E93, 042117 (2016)

work page 2016
[49]

Lefevre and G

A. Lefevre and G. Biroli, J. Stat. Mech.: Theory Exp. 2007, P07024 (2007)

work page 2007
[50]

End Matter Derivation of the Reggeon field theory From Eq

Discussions about the barrier effect can be found in SI, and we show that the reaction rule respresenting bar- rier effect should share the similar form of Reggeon field equations with third orderρ A nonlinearity. End Matter Derivation of the Reggeon field theory From Eq. 3, the corresponding action can be formally given byS[{ˆa, a,ˆp, p}] =R ddx R +∞ −∞ ...

work page