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arxiv: 2606.08004 · v1 · pith:MVNYPACTnew · submitted 2026-06-06 · ❄️ cond-mat.stat-mech · cond-mat.mtrl-sci

Tracking metastable phases by complex Lee-Yang zeros

Yi-Hua Dong , Ling Liu , Fang-Cheng Wang , Qi-Jun Ye , Xin-Zheng Li This is my paper

Pith reviewed 2026-06-27 19:22 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech cond-mat.mtrl-sci
keywords metastable phasesLee-Yang zeroscomplex thermal fieldsperiodically driven systemsphase diagramsnon-equilibrium statesdensity of states
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The pith

Metastable phases exist in the complex plane of thermal fields as regions delineated by Lee-Yang zeros.

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

The paper shows that metastable phases, normally suppressed in equilibrium diagrams, can be located as regions in the complex plane of thermal fields that are bounded by Lee-Yang zeros. This is demonstrated numerically in a toy model whose density of states has three tunable Gaussian peaks and in a periodically driven system. As the artificial parameter or drive amplitude is increased, the zeros that bound the metastable region move toward the real axis and split into separate branches, marking the stabilization of the metastable phase inside the gap between two stable phases. In the driven system the imaginary parts of the zeros scale with drive strength, connecting the approach to non-equilibrium control. The result supplies a concrete scheme for including metastable phases in phase-diagram analysis.

Core claim

Metastable phases exist in the complex plane of thermal fields, as regions delineated by Lee-Yang zeros (LYZs). In both a toy model with a tunable density of states and a periodically driven system, increasing the artificial parameter or drive amplitude causes the LYZs that bound the metastable phase to approach the real axis and split into separated branches. This splitting signals the emergence and stabilization of the metastable phase inside the enlarged gap between two adjacent stable phases. The imaginary part of the LYZs correlates with drive strength.

What carries the argument

Lee-Yang zeros in the complex plane of thermal fields, which move and split to mark the boundaries of metastable regions.

If this is right

  • As control parameters grow, Lee-Yang zeros approach the real axis and split, indicating stabilization of the metastable phase.
  • The imaginary part of the zeros scales directly with drive amplitude in periodically driven systems.
  • Periodic drives can be reinterpreted as complex thermal fields for phase-diagram construction.
  • The same bounding mechanism supplies a practical route to mapping metastable phases that are invisible on the real axis.

Where Pith is reading between the lines

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

  • The same zero-tracking procedure could be tested on other non-equilibrium protocols such as sudden quenches or stochastic driving.
  • Experimental measurement of Lee-Yang zeros in driven systems might allow direct readout of metastable lifetimes.
  • If the splitting pattern generalizes, it could guide the design of drive protocols that deliberately enlarge metastable regions.

Load-bearing premise

The numerically observed movement and splitting of Lee-Yang zeros correctly identifies the boundaries of metastable phases rather than arising as an artifact of the chosen density of states or drive protocol.

What would settle it

In the toy model, if raising the tunable parameter leaves the Lee-Yang zeros stationary or prevents them from splitting, the claim that their motion tracks metastable-phase boundaries would be falsified.

Figures

Figures reproduced from arXiv: 2606.08004 by Fang-Cheng Wang, Ling Liu, Qi-Jun Ye, Xin-Zheng Li, Yi-Hua Dong.

Figure 1
Figure 1. Figure 1: FIG. 1: The three-Gaussian-peak model with (a)-(d) the referenced DOS distribution [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: The energy probability distribution [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
read the original abstract

Metastable phases (MPs) are energetically unfavorable states typically suppressed in equilibrium phase diagrams. Rather than remaining ''hidden'', we show that they exist in the complex plane of thermal fields, as regions delineated by Lee-Yang zeros (LYZs). We demonstrate this numerically in a toy model with a tunable density of states featuring three Gaussian peaks and in a more realistic periodically driven system. In both cases, as artificial parameters or drive amplitudes increase, the LYZs bounding the MP approach the real axis and split into separated branches, signaling the emergence and stabilization of the MP within the enlarged gap between two adjacent stable phases. In the driven system, the imaginary part of LYZs correlates with drive strength, linking Lee-Yang theory to terahertz matter manipulation. These findings provide a scheme to describe MPs in phase diagram analysis. By viewing periodic drives as complex thermal fields, it also offers a new perspective for understanding and engineering non-equilibrium collective states.

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 claims that metastable phases exist as regions in the complex plane of thermal fields, delineated by Lee-Yang zeros (LYZs). This is shown numerically in a toy model whose density of states consists of three tunable Gaussian peaks and in a periodically driven system; in both cases, increasing artificial parameters or drive amplitudes causes the LYZs that bound the metastable phase to approach the real axis and split into separated branches, signaling stabilization of the metastable phase in the gap between stable phases. In the driven case the imaginary part of the LYZs is reported to correlate with drive strength.

Significance. If the numerical correspondence between LYZ splitting and metastability generalizes beyond the specific models, the work would supply a concrete scheme for locating metastable phases within complex-field phase diagrams and would connect equilibrium Lee-Yang theory to non-equilibrium periodic driving, offering a perspective for terahertz control of collective states.

major comments (1)
  1. [Abstract; toy-model and driven-system numerical sections] The central claim that LYZ-bounded regions delineate metastable phases rests entirely on numerical trajectories observed in two constructions: a three-Gaussian DOS toy model and one specific periodic-drive protocol. No analytic derivation is supplied showing that LYZ splitting must occur precisely when a metastable state appears (as opposed to being an artifact of the chosen functional form of the DOS or the drive waveform). If an alternative DOS (e.g., Lorentzians of different widths) or a different drive protocol produces qualitatively different LYZ motion while preserving the underlying metastability, the proposed delineation would not be a general signature.
minor comments (1)
  1. [Abstract] The abstract refers to “artificial parameters or drive amplitudes” without giving their explicit functional forms or ranges, which hinders immediate reproducibility of the reported LYZ trajectories.

Simulated Author's Rebuttal

1 responses · 1 unresolved

We thank the referee for the detailed reading and constructive criticism. We address the major comment below, acknowledging the numerical nature of the evidence while defending the choice of models as representative for the demonstration.

read point-by-point responses

  1. Referee: [Abstract; toy-model and driven-system numerical sections] The central claim that LYZ-bounded regions delineate metastable phases rests entirely on numerical trajectories observed in two constructions: a three-Gaussian DOS toy model and one specific periodic-drive protocol. No analytic derivation is supplied showing that LYZ splitting must occur precisely when a metastable state appears (as opposed to being an artifact of the chosen functional form of the DOS or the drive waveform). If an alternative DOS (e.g., Lorentzians of different widths) or a different drive protocol produces qualitatively different LYZ motion while preserving the underlying metastability, the proposed delineation would not be a general signature.

    Authors: We agree that the central claim relies on numerical observations in two specific constructions without an accompanying analytic derivation. The three-Gaussian DOS was chosen because it is a standard, analytically tractable toy model that permits independent tuning of peak positions, widths, and amplitudes to control the appearance and stabilization of a central metastable phase; the LYZ splitting is observed to occur exactly when the central peak height is increased to make that phase locally stable. The periodic-drive protocol is a concrete, experimentally relevant Floquet example. We have not examined Lorentzian DOS forms or alternative waveforms, so we cannot exclude the possibility that the LYZ motion is sensitive to these choices. In the revised manuscript we will insert explicit caveats in the abstract, the toy-model section, the driven-system section, and the conclusions stating that the reported delineation is a numerical finding within the models considered and that its status as a general signature remains to be established by future analytic work or broader numerical tests. revision: yes

standing simulated objections not resolved
  • Providing an analytic derivation establishing that LYZ splitting must occur for arbitrary density-of-states forms and drive protocols whenever a metastable phase appears

Circularity Check

0 steps flagged

No circularity: numerical demonstration in specific models

full rationale

The paper's central claim is established by direct numerical simulation of LYZ trajectories in a toy model (three-Gaussian DOS) and a periodically driven system, showing LYZs approaching the real axis and splitting with increasing parameters. No equations, predictions, or uniqueness theorems are presented that reduce by construction to fitted inputs, self-citations, or ansatzes imported from prior author work. The derivation chain consists of model construction followed by observation; it does not rename known results or force outcomes via self-referential fitting. This is a standard self-contained numerical study.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are stated. The central claim rests on the unexamined assumption that Lee-Yang zeros delineate metastable regions in the models used.

pith-pipeline@v0.9.1-grok · 5705 in / 1097 out tokens · 17093 ms · 2026-06-27T19:22:55.622364+00:00 · methodology

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