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arxiv: 2605.19964 · v1 · pith:EBZAXJRPnew · submitted 2026-05-19 · ✦ hep-ph

Lee-Yang zeros and edge singularity in a mean-field approach

Tatsuya Wada , Gy\H{o}z\H{o} Kov\'acs , Masakiyo Kitazawa , Takahiro M. Doi This is my paper

Pith reviewed 2026-05-20 04:20 UTC · model grok-4.3

classification ✦ hep-ph
keywords Lee-Yang zeroscritical pointQCDmean-field modelfinite-size scalingedge singularitycomplex chemical potentialpartition function
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0 comments X

The pith

In a minimal mean-field QCD model with finite-size effects, Lee-Yang zeros locate the critical point when corrections from irrelevant operators are included.

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

This paper examines the analytic structure of the partition function in a minimal mean-field effective model of QCD that incorporates finite-volume corrections, at complex chemical potentials. It tracks the temperature dependence of Lee-Yang zeros for different system sizes and shows their connection to the edge singularity. Several finite-size scaling methods based on these zeros and on susceptibility ratios are compared for locating the critical point. The methods identify the critical point successfully, but only when corrections from irrelevant operators receive careful treatment.

Core claim

In the minimal mean-field effective model of QCD with finite-size effects, the temperature dependence of Lee-Yang zeros and their relation to the edge singularity enable finite-size scaling methods using these zeros and susceptibility ratios to identify the critical point, though accurate determination requires careful treatment of corrections from irrelevant operators.

What carries the argument

Lee-Yang zeros of the partition function in the complex chemical potential plane, analyzed via their temperature dependence, finite-size scaling, and connection to the edge singularity.

If this is right

  • Finite-size scaling of Lee-Yang zeros successfully identifies the critical point.
  • Susceptibility ratio methods also locate the critical point in the model.
  • Corrections from irrelevant operators are required for accurate determination of the critical point location.
  • The zeros move toward the edge singularity as temperature and system size vary.

Where Pith is reading between the lines

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

  • The same scaling approach might be tested on lattice QCD data at imaginary chemical potential to cross-check critical point estimates.
  • If the mean-field picture holds near the critical region, zero-based methods could help reduce systematic uncertainties in full QCD calculations.
  • Extending the model to include additional degrees of freedom would test whether the edge singularity identification remains stable.

Load-bearing premise

The minimal mean-field effective model of QCD with finite-size effects incorporated accurately captures the analytic structure of the partition function at complex chemical potentials that is relevant for locating the critical point.

What would settle it

Observation that the critical point extracted from Lee-Yang zero scaling differs substantially from the value obtained after including irrelevant operator corrections, or fails to agree with susceptibility ratio results, would show the methods do not determine the point accurately.

Figures

Figures reproduced from arXiv: 2605.19964 by Gy\H{o}z\H{o} Kov\'acs, Masakiyo Kitazawa, Takahiro M. Doi, Tatsuya Wada.

Figure 1
Figure 1. Figure 1: Phase diagram of the single-component quark-meson [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: Comparison of various definitions of the pseudo [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 2
Figure 2. Figure 2: Trajectories of the first LYZs µ (1) LY(T, L) for L = 8, 12, 16 fm (dashed lines) and the LYES µES(T) (solid line) in the complex µB plane for the parameter set A (top) and set B (bottom). The locations at several temperatures are indicated by different markers. The dotted line represents Im µB = Re µB. satisfying |ZN(T, µB, L)| = 0. For a search for LYZs at a continuous range of T, we vary T with a small … view at source ↗
Figure 4
Figure 4. Figure 4: Trajectories of the first LYZs µ (1) LY(T, L) for L = 8, 12, 16 fm (dashed lines) and the LYES µES(T) (solid line) in the complex µ 2 B plane. The meanings of lines and markers are the same as those in [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: Lee–Yang zero ratios Rn1(T, L) at L = 6, 8, 10, 12, 14, and 16 fm. From top to bottom, the panels show R21(T, L), R31(T, L), and R41(T, L), respectively. Markers indicate intersection points for pairs of adjacent volumes, with their colors corresponding to the larger volume in each pair. The vertical and horizontal dashed lines indicate TCP and the value of the intersection point rn1 for L → ∞, respectivel… view at source ↗
Figure 9
Figure 9. Figure 9: System-size dependence of Rn1(TCP, L)/rn1 and B4(TCP, L)/b4 as functions of 1/L for L = 8–24 fm at TCP = 121.5348 MeV. The diamond and circle markers denote Rn1(TCP, L)/rn1 and B4(TCP, L)/b4, respectively, while the dashed and dotted lines show the fit results to these values. of the irrelevant operators alter Eqs. (7) and (10), and it gives rise to additional L-dependent terms in Eqs. (30), (31), and (35)… view at source ↗
Figure 7
Figure 7. Figure 7: Scaled LYZs L yh Im µ (n) LY (T, L) at L = 6, 8, 10, 12, 14, and 16 fm, with the top and bottom panels corresponding to n = 1 and n = 2, respectively. T [MeV] 120 121 122 123 124 𝓑 4 ( T ,L ) 2.18 2.20 2.22 L [fm] 6 8 10 12 14 16 (TCP, b4) [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Fourth-order Binder cumulant B4(T, L) for L = 6, 8, · · · , 16 fm. The horizontal dashed line indicates b4, the value of the intersection point for L → ∞. shows that Rn1(TCP, L)/rn1 decreases and pass through Rn1(TCP, L)/rn1 = 1 at L ≃ 12 fm, but then turn to approach to unity for L ≳ 20 fm. At present, we consider that this behavior at large L comes from the modification of the FSS relations due to irrele… view at source ↗
read the original abstract

The analytic structure of the partition function in finite-volume systems is investigated at complex chemical potentials in a minimal mean-field effective model of QCD with finite-size effects incorporated. We discuss the temperature dependence of the Lee-Yang zeros and their relation to the edge singularity for various system sizes. Different methods for locating the critical point based on finite-size scaling of Lee-Yang zeros and susceptibility ratios are compared. We demonstrate that these methods can successfully identify the critical point, whereas a careful treatment of corrections from irrelevant operators is crucial for its accurate determination.

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 / 2 minor

Summary. The manuscript investigates the analytic structure of the partition function in a minimal mean-field effective model of QCD with finite-size effects at complex chemical potentials. It analyzes the temperature dependence of Lee-Yang zeros and their relation to the edge singularity for different system sizes. Different finite-size scaling methods based on Lee-Yang zeros and susceptibility ratios are compared for locating the critical point, with the demonstration that these methods identify the known critical point once corrections from irrelevant operators are included.

Significance. If the results hold, the work offers a controlled benchmark in a solvable mean-field model for validating finite-size scaling techniques that locate critical points via Lee-Yang zeros. It explicitly shows the necessity of accounting for corrections from irrelevant operators, which strengthens the reliability of such methods and may guide their application in lattice QCD or experimental contexts. The direct comparison to the model's known critical point is a clear strength of the analysis.

major comments (1)
  1. The central claim that corrections from irrelevant operators are crucial for accurate determination of the critical point would be strengthened by a quantitative comparison (e.g., deviation from the known critical chemical potential with and without the corrections) in the section presenting the susceptibility ratio and Lee-Yang zero scaling results.
minor comments (2)
  1. The abstract could briefly specify the form of the mean-field effective potential or the key parameters entering the model to orient readers.
  2. Figure captions for the plots of Lee-Yang zeros versus temperature should explicitly list the system sizes and the values of any fixed parameters used.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive assessment of our work and the constructive suggestion. We address the major comment below and have revised the manuscript to incorporate the recommended quantitative comparison.

read point-by-point responses

  1. Referee: The central claim that corrections from irrelevant operators are crucial for accurate determination of the critical point would be strengthened by a quantitative comparison (e.g., deviation from the known critical chemical potential with and without the corrections) in the section presenting the susceptibility ratio and Lee-Yang zero scaling results.

    Authors: We agree that a direct quantitative comparison would strengthen the presentation of our central claim. In the revised manuscript we have added a new table in the section on finite-size scaling methods that reports the extracted critical chemical potential for both the susceptibility-ratio and Lee-Yang-zero approaches, with and without the inclusion of corrections from irrelevant operators. The table lists the absolute and relative deviations from the known mean-field critical value for several system sizes. These numbers show that the deviations are reduced by roughly an order of magnitude once the corrections are taken into account, thereby providing explicit support for the necessity of including them. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained within the model study

full rationale

The paper performs a controlled numerical and scaling analysis inside a minimal mean-field effective model of QCD whose critical point is known by construction. Finite-size Lee-Yang zeros and susceptibility ratios are computed directly from the model's partition function at complex chemical potentials; the scaling relations and corrections from irrelevant operators are applied to recover the model's own critical point. No load-bearing step reduces a prediction to a fitted parameter by definition, nor does any central claim rest on a self-citation chain that itself lacks independent verification. The model parameters and ansatz are stated explicitly as part of the effective theory setup rather than derived from the target result. This is the standard honest outcome for a model-study paper whose conclusions are benchmarked against the model's internal critical point.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The study rests on the domain assumption that the chosen mean-field model reproduces the relevant analytic properties of QCD at complex chemical potential; no free parameters or invented entities are mentioned in the abstract.

axioms (1)
  • domain assumption The minimal mean-field effective model of QCD with finite-size effects accurately represents the partition function's analytic structure at complex chemical potentials.
    This modeling choice underpins every numerical result and comparison reported in the abstract.

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