{"id":"c0ffcd18-5254-49d3-b4c6-239ac7fe02a2","arxiv_id":"2606.08004","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Metastable phases are delineated by Lee-Yang zeros in the complex thermal-field plane, shown numerically in a three-Gaussian toy model and a periodically driven system where zeros approach the real axis with increasing drive.","lead":"The paper claims metastable phases appear as regions in the complex plane of thermal fields, bounded by Lee-Yang zeros. This framing could link equilibrium phase diagrams to driven non-equilibrium states in materials.","discovery_kind":"new_application","skeptic_critique":{"model":"grok-4.3","headline":"LYZ movement/splitting may be tied to specific Gaussian DOS or drive protocol rather than general MP signature","rationale":"The reader's weakest assumption directly identifies the same numerical-artifact risk. Because the manuscript supplies only model-specific numerics without cross-checks on DOS shape or drive protocol, the concern stands and the provisional UNVERDICTED status is appropriate.","tokens_in":1649,"tokens_out":354,"duration_ms":11653,"concrete_test":"Recompute the Lee-Yang zeros for the toy model after replacing the three-Gaussian DOS with three Lorentzians of matched widths and centers; if the splitting pattern or the gap enlargement changes while the expected metastable regime (identified by independent lifetime or barrier-height calculation) remains the same, the LYZ criterion is not robust.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim requires that LYZ-bounded regions in the complex plane correspond to metastable phases. This rests on numerical observation that LYZs approach the real axis and split as parameters increase in (i) a toy model whose DOS consists of three tunable Gaussians and (ii) a periodically driven system. For the interpretation to be load-bearing, the splitting must reflect the physical emergence of a metastable state rather than a feature induced by the chosen functional form of the DOS or the specific periodic drive. No analytic derivation is supplied showing why LYZ splitting must occur precisely when a metastable phase appears; the evidence is therefore the numerical behavior in these two constructions. If an alternative DOS (e.g., Lorentzians of different widths) or a different drive waveform produces qualitatively different LYZ trajectories without altering the underlying metastability, the delineation would be an artifact.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","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.","tokens_in":1806,"tokens_out":411,"duration_ms":15533,"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":[{"comment":"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.","section":"Abstract; toy-model and driven-system numerical sections"}],"minor_comments":[{"comment":"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.","section":"Abstract"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"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.","responses":[{"response":"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_made":"yes","referee_comment":"[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."}],"tokens_in":1316,"tokens_out":430,"duration_ms":15944,"standing_objections":["Providing an analytic derivation establishing that LYZ splitting must occur for arbitrary density-of-states forms and drive protocols whenever a metastable phase appears"]},"desk_editor":{"model":"grok-4.3","letter":"The main takeaway is that metastable phases get marked out as regions in the complex thermal-field plane by the movement and splitting of Lee-Yang zeros. They demonstrate this in a toy model whose density of states is three tunable Gaussians and in a periodically driven system, where the zeros approach the real axis and separate as the drive or artificial parameter grows, leaving a gap they associate with the metastable state. In the driven case the imaginary part of the zeros tracks drive strength, which they tie to terahertz manipulation.\n\nWhat works is the concrete numerical observation that the zeros behave this way in both setups and the suggestion that periodic drives can be read as complex fields. That gives a visual scheme for locating metastable phases inside phase diagrams.\n\nThe soft spot is the lack of any analytic reason why the splitting must occur exactly when a metastable phase stabilizes. Everything rests on the chosen Gaussian form and the particular drive waveform. If a different density of states or drive produces different zero trajectories while the underlying metastability stays the same, the delineation would be an artifact of the construction rather than a general signature. No broader test or derivation is supplied to rule that out.\n\nThis is for people already working on Lee-Yang zeros, metastable states, or driven matter who want a new descriptive tool to play with. It is worth sending to peer review so referees can check whether the pattern survives changes in the density of states or drive protocol.","headline":"The paper shows numerically that Lee-Yang zeros split and approach the real axis in a Gaussian-DOS toy model and a driven system as metastable phases appear, but the pattern may be tied to those specific choices rather than a general rule.","tokens_in":2289,"tokens_out":378,"would_cite":false,"duration_ms":14990,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Metastable phases exist in the complex plane of thermal fields as regions delineated by Lee-Yang zeros.","keywords":["metastable phases","Lee-Yang zeros","complex thermal fields","periodically driven systems","phase diagrams","non-equilibrium states","density of states"],"falsifier":"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.","tokens_in":2556,"feed_emoji":"","tokens_out":690,"duration_ms":19624,"temperature":0.7,"pith_summary":"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.","feed_headline":"Lee-Yang zeros mark metastable phases in complex plane","feed_subtitle":"Zeros approach the real axis and split as drive strength rises, locating hidden phases in both toy and driven models.","key_machinery":"Lee-Yang zeros in the complex plane of thermal fields, which move and split to mark the boundaries of metastable regions.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"fun_headline_variants":["Lee-Yang zeros bound metastable phases in complex thermal fields","Metastable phases located by Lee-Yang zeros in complex plane","Lee-Yang zeros split as metastable phases stabilize","Imaginary Lee-Yang zeros correlate with drive in metastable phases"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Lee-Yang zeros bound metastable phases in complex thermal fields","Metastable phases located by Lee-Yang zeros in complex plane","Lee-Yang zeros split as metastable phases stabilize","Imaginary Lee-Yang zeros correlate with drive in metastable phases"]},"model":"grok-4.3","cost_usd":0.003904,"raw_usage":{"total_tokens":1987,"prompt_tokens":636,"num_sources_used":0,"completion_tokens":59,"cost_in_usd_ticks":39037000,"prompt_tokens_details":{"text_tokens":636,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1292,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":636,"tokens_out":59,"duration_ms":7528,"temperature":1.0,"reasoning_tokens":1292,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-27T19:22:55.622364+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"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.","supporting_citations":[],"review_version":1}