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arxiv: 2507.06023 · v4 · submitted 2025-07-08 · ❄️ cond-mat.stat-mech · cond-mat.soft

Liquid-Gas Criticality of Hyperuniform Fluids

Shang Gao , Hao Shang , Hao Hu , Yu-Qiang Ma , Qun-Li Lei This is my paper

Pith reviewed 2026-05-19 05:59 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech cond-mat.soft
keywords liquid-gas transitionhyperuniform fluidsnon-equilibrium criticalityuniversality classactive matterfluctuation-dissipation relationrenormalization group
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0 comments X

The pith

Non-equilibrium hyperuniform fluids with center-of-mass conservation show liquid-gas criticality outside the Ising class.

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

The paper proves that hyperuniform fluids in non-equilibrium settings with extra conservation laws have a liquid-gas phase transition that does not follow the usual Ising universality. This matters because it shows non-equilibrium effects can change fundamental critical behavior. In two dimensions, the critical point has finite density fluctuations but still diverging compressibility, making it calm yet responsive. The analysis uses renormalization group methods on a generalized model to show the upper critical dimension drops from four to two.

Core claim

Non-equilibrium hyperuniform fluids with additional center-of-mass conservation exhibit liquid-gas criticality different from the Ising universality class. Hyperuniformity reduces the upper critical dimension from 4 to 2. At the critical point in 2D, density fluctuations remain finite with S(q) ~ q^0 while compressibility diverges, violating the conventional fluctuation-dissipation relation through a scale-dependent effective temperature T_eff(q) proportional to q squared.

What carries the argument

A generalized Model B dynamics incorporating a scale-dependent effective temperature T_eff(q) ∝ q² in the fluctuation-dissipation relation.

Load-bearing premise

The system obeys a generalized Model B with an effective temperature that scales as the square of the wavevector in the fluctuation-dissipation relation.

What would settle it

Measuring density structure factor S(q) at the critical point in a two-dimensional hyperuniform fluid showing it approaches a constant rather than diverging as in equilibrium Ising systems.

Figures

Figures reproduced from arXiv: 2507.06023 by Hao Hu, Hao Shang, Qun-Li Lei, Shang Gao, Yu-Qiang Ma.

Figure 1
Figure 1. Figure 1: FIG. 1: (a) Schematic of dissipation-induced phase separation (DIPS) of active spinners, where particle color (from blue to red) [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Hydrodynamic theory of active spinner: (a) Theoretical prediction of average collision frequency [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Simulation results of 2D stochastic field. (a) structure factor for system at different distance from critical point [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: The spinodal decomposition and coarsening process of (a) active spinner fluids ( [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
read the original abstract

In statistical physics, it is well established that the liquid-gas (LG) phase transition with divergent critical fluctuations belongs to the Ising universality class. Whether non-equilibrium effects can alter this universal behavior remains a fundamental open question. In this work, we theoretically prove that non-equilibrium hyperuniform (HU) fluids with additional center-of-mass conservation exhibit LG criticality different from the Ising universality class. As a specific case, we investigate a 2D HU fluid composed of active spinners, where phase separation is driven by dissipative collisions. Strikingly, at the critical point, the 2D HU fluid displays finite density fluctuations $S(q)\sim q^{\eta}$ with $\eta=0$, while the compressibility still diverges. The critical point is thus calm yet highly susceptible, in fundamental violation of the conventional fluctuation-dissipation relation. Consistently, we observe short-range pair correlation functions coexisting with quasi-long-range response functions at the critical point. Based on a generalized Model B and renormalization-group analysis, we prove that hyperuniformity reduces the upper critical dimension $d_c$ from $4$ to $2$. Moreover, the critical point exhibits Gaussian density fluctuations and non-divergent energy fluctuations. Furthermore, the HU fluid undergoes non-conventional spinodal decomposition. The origin of the above anomalies lies in the non-equilibrium nature of the system which obeys a generalized fluctuation-dissipation relation $2\mathrm{Im}~ \chi(q,\omega) ={\omega }C(q,\omega)/{k_B T_{\text{eff}}(q)}$ with a scale-dependent effective temperature $T_{\rm eff}(q) \propto q^2$. These findings establish a striking exception to conventional paradigms of critical phenomena and illustrate how non-equilibrium forces can fundamentally reshape universality classes.

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

2 major / 2 minor

Summary. The manuscript claims to prove that non-equilibrium hyperuniform fluids with center-of-mass conservation exhibit liquid-gas criticality outside the Ising class. For the specific case of 2D active spinners with dissipative collisions, it reports that at criticality the structure factor remains finite with S(q)∼q^η (η=0) while compressibility diverges, that hyperuniformity lowers the upper critical dimension from 4 to 2, and that the system displays Gaussian density fluctuations together with non-conventional spinodal decomposition. These results are obtained from a generalized Model B whose noise correlator is fixed by a scale-dependent effective temperature T_eff(q)∝q² entering the generalized fluctuation-dissipation relation 2 Im χ(q,ω)=ω C(q,ω)/k_B T_eff(q).

Significance. If the q² scaling of T_eff(q) is independently justified by the microscopic dynamics, the work would constitute a clear example of a non-equilibrium mechanism that changes the universality class of liquid-gas criticality and reduces the upper critical dimension, with the unusual combination of finite fluctuations and divergent susceptibility. The RG analysis and the explicit contrast with equilibrium Ising behavior are the strongest elements.

major comments (2)
  1. [Generalized Model B and RG analysis (around the definition of the noise term and the FDR)] The reduction of d_c from 4 to 2 and the resulting η=0 fixed point are direct consequences of the noise correlator set by T_eff(q)∝q² in the generalized FDR. The manuscript must demonstrate that this specific q-dependence follows from the collision rules of the active-spinner model rather than being chosen to produce hyperuniformity; otherwise the central claim that hyperuniformity itself lowers d_c becomes circular. This issue is load-bearing for the entire RG analysis.
  2. [Introduction and abstract statement of the FDR] The abstract states that the anomalies 'lie in the non-equilibrium nature of the system which obeys' the generalized FDR with T_eff(q)∝q². If this relation is postulated rather than derived from the microscopic equations of motion for the spinners, the proof that the 2D HU fluid belongs to a new class does not yet apply to the physical system described in the introduction.
minor comments (2)
  1. [Discussion of pair correlations] Clarify whether the pair-correlation functions are strictly short-ranged or exhibit power-law tails at the critical point; the current wording is ambiguous.
  2. [Results section] Add a brief comparison table or plot contrasting the critical exponents obtained here with those of equilibrium Model B and Ising in d=2 and d=3.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review of our manuscript. The comments highlight important points regarding the microscopic justification of the generalized fluctuation-dissipation relation, which we address in detail below. We have revised the manuscript to strengthen the presentation of the derivation from the active-spinner dynamics.

read point-by-point responses

  1. Referee: The reduction of d_c from 4 to 2 and the resulting η=0 fixed point are direct consequences of the noise correlator set by T_eff(q)∝q² in the generalized FDR. The manuscript must demonstrate that this specific q-dependence follows from the collision rules of the active-spinner model rather than being chosen to produce hyperuniformity; otherwise the central claim that hyperuniformity itself lowers d_c becomes circular. This issue is load-bearing for the entire RG analysis.

    Authors: We agree that the microscopic origin of T_eff(q) ∝ q² must be clearly established to avoid any appearance of circularity. In the manuscript, this scaling is not postulated but derived from the center-of-mass conservation and dissipative collision rules of the 2D active-spinner model. Starting from the microscopic equations of motion for the spinners (Section II), we perform a coarse-graining procedure that yields the hydrodynamic description. The absence of momentum conservation combined with center-of-mass conservation produces a noise correlator whose strength scales as q², leading to the scale-dependent effective temperature in the generalized FDR. This derivation is independent of the subsequent RG analysis and is confirmed by direct comparison with particle simulations of the spinner model. To address the concern explicitly, we have added a dedicated subsection (now Section III.B) that walks through the mapping from collision rules to the noise term step by step, including the explicit calculation of the correlator. This makes clear that hyperuniformity and the modified FDR both emerge from the same microscopic conservation law, but the FDR form is fixed prior to the RG treatment. The reduction of the upper critical dimension therefore follows directly from the non-equilibrium dynamics of the physical system rather than from an arbitrary choice. revision: yes

  2. Referee: The abstract states that the anomalies 'lie in the non-equilibrium nature of the system which obeys' the generalized FDR with T_eff(q)∝q². If this relation is postulated rather than derived from the microscopic equations of motion for the spinners, the proof that the 2D HU fluid belongs to a new class does not yet apply to the physical system described in the introduction.

    Authors: The abstract is intended as a concise summary of the central result. However, we acknowledge that its phrasing could be read as implying the FDR is introduced without derivation. In the full manuscript, the generalized FDR with T_eff(q) ∝ q² is obtained by coarse-graining the microscopic dynamics of the active spinners with dissipative collisions, as detailed in Sections II and III. We have now revised the abstract to read: 'These findings establish a striking exception... which obeys a generalized fluctuation-dissipation relation... with a scale-dependent effective temperature T_eff(q) ∝ q² derived from the center-of-mass conserving microscopic dynamics.' This change ensures the abstract accurately reflects that the relation is derived rather than assumed, thereby connecting the RG results directly to the physical spinner system introduced in the opening paragraphs. The revision is limited to wording and does not alter any technical content. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation proceeds from explicit model assumptions via RG analysis

full rationale

The paper defines a generalized Model B incorporating the stated scale-dependent T_eff(q) in the fluctuation-dissipation relation as the starting dynamical framework for non-equilibrium hyperuniform fluids. It then applies renormalization-group analysis to this model to obtain the reduced upper critical dimension, Gaussian fluctuations with η=0, and diverging compressibility. These outcomes are computed consequences of the RG flow under the given noise correlator rather than presupposed by redefining the input or fitting parameters to match the target scaling. No step reduces the claimed critical behavior to a tautological restatement of the initial ansatz or to a self-citation whose content is unverified; the derivation remains self-contained within the stated effective theory.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The central claims rest on the introduction of a generalized Model B dynamics and a scale-dependent effective temperature whose form is tied to the non-equilibrium driving; no free parameters are explicitly fitted in the abstract, but the effective temperature function acts as an additional assumption.

axioms (2)
  • domain assumption The system obeys a generalized fluctuation-dissipation relation with scale-dependent T_eff(q) ∝ q².
    Invoked in the abstract as the origin of the anomalies and the violation of conventional FDR.
  • domain assumption Hyperuniformity imposes an additional center-of-mass conservation law that modifies the hydrodynamic description.
    Stated as the key non-equilibrium feature distinguishing the fluid from equilibrium cases.
invented entities (1)
  • scale-dependent effective temperature T_eff(q) no independent evidence
    purpose: To encode the non-equilibrium driving and produce the modified critical scaling and FDR violation.
    Introduced to explain the finite density fluctuations and diverging compressibility; no independent falsifiable prediction outside the model is given in the abstract.

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Forward citations

Cited by 1 Pith paper

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