{"id":"a7016790-9961-4327-a6d4-bb8c9eeb6270","arxiv_id":"hep-lat/0106002","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"A first lattice QCD calculation places the critical endpoint of the QCD phase diagram at temperature 160 MeV and baryon chemical potential 725 MeV, using reweighting from zero chemical potential and Lee-Yang zero scaling.","lead":"QCD is expected to have a critical endpoint in the temperature versus chemical potential plane, where a smooth crossover becomes a sharp phase transition. This paper reports the first lattice QCD estimate of its location: temperature 160 MeV and baryon chemical potential 725 MeV.","discovery_kind":"new_method","skeptic_critique":{"model":"selfhosted/deepseek-v4.1-flash","headline":"The endpoint µ_end = 0.375(20) is read off a linear fit to Im(β∞) vs µ that is known to overshoot (Im = -0.25(10) at µ=0.4); the fit's inadequacy inflates the quoted error but does not correct the central value.","rationale":"The reader's weakest_assumption correctly locates the load-bearing issue: the endpoint is extracted from a linear fit to Im(β∞) vs µ, the fit produces an unphysical negative value at µ=0.4, and the systematic error is estimated from that same overshoot. I agree with this diagnosis and with the CONDITIONAL verdict. The paper is an honest exploratory first determination; the method (reweighting plus Lee-Yang zeros) is a genuine contribution, and the authors explicitly list the coarse lattice, heavy light quarks, and missing continuum/chiral/step-size extrapolations as open items. The concern is not that the method is unsound but that the central value µ_end = 0.375(20) is model-dependent: the linear fit is known to fail at the largest µ, and the quoted ±0.20 is dominated by a systematic derived from that failure rather than from an independent estimate. A non-linear fit consistent with critical scaling could move the crossing. I would add one secondary point the reader mentions only in passing: the V→∞ extrapolation β0(V) = β∞0 + ζ/V is not clean at small µ (the Ls=6 point at µ=0.1 lies well above the line through Ls=4 and Ls=8), although it is more consistent near the endpoint where the errors are larger. Separately, the physical-scale conversion carries a spread of roughly 15–20% among R0, mρ, and √σ at the two β values in Table 1 (e.g. at β=5.208 the three give a ≈ 0.26, 0.31, 0.26 fm), which is larger than the quoted ±3.5 MeV on T_E and ±35 MeV on µ_E; this is partly covered by the acknowledged continuum extrapolation but is not reflected in the abstract's error bars. Neither point overturns the paper's status as a first ab initio estimate, so the verdict should remain CONDITIONAL rather than move to ACCEPT or REJECT. The concrete test above (non-linear refit of the µ-dependence) is the single check most likely to settle whether the quoted endpoint survives a more realistic fitting form.","tokens_in":9365,"tokens_out":16825,"duration_ms":341112,"concrete_test":"Refit the four Im(β∞) points (µ = 0.1, 0.2, 0.3, 0.4) with a physically motivated non-linear form, e.g. Im = A(µ_E - µ)^β with β free, or a quadratic in µ, and recompute the zero crossing. If µ_end moves by more than the quoted ±0.20, the endpoint is not determined to the stated precision and the linear-fit central value should be replaced by a model-spread range.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The endpoint is defined as the µ at which the extrapolated Im(β∞) crosses zero. The paper fits Im(β∞) linearly in µ and reports µ_end = 0.375(20). The fit is known to be inadequate: at µ=0.4 it gives Im = -0.25(10), a negative imaginary part of a Lee-Yang zero, which is unphysical. The crossing at 0.375 is essentially a two-point interpolation between µ=0.3 (Im = 0.74 ± 0.19) and µ=0.4 (Im = -0.25 ± 0.10). Propagating those errors through the linear interpolation gives a statistical uncertainty of only ~0.009; the quoted ±0.20 is therefore dominated by the systematic estimated from the overshoot itself. That is the self-referential step: the fit's own residual is used to set the error, but the central value is still taken from the fit that produced the residual. Near a critical endpoint the Lee-Yang zero should vanish as (µ_E - µ)^β with β not necessarily unity, so a linear fit is a proxy whose crossing can shift once curvature is included. The paper acknowledges the overshoot ('slightly overshoots') and cites the electroweak precedent, but does not show that the central value is stable under a non-linear fit. A secondary, related soft spot is the V→∞ extrapolation: at µ=0.1 the Ls=6 point (2.66 ± 0.06) sits far above the line through Ls=4 and Ls=8, so leading 1/V scaling is not clean at small µ (it is better near the endpoint, where errors are larger). The endpoint determination therefore rests on a fit whose functional form is not validated by the data it is fitted to.","agreement_with_reader":"agree"},"referee_report":{"model":"selfhosted/deepseek-v4.1-flash","summary":"The paper reports a lattice determination of the QCD critical endpoint in n_f = 2+1 staggered QCD with semi-realistic quark masses on L_t = 4 lattices. The method combines reweighting in the chemical potential and gauge coupling from μ = 0 transition configurations (the authors' earlier proposal, Ref. [13]) with an exact evaluation of the quark determinant as a function of μ via the eigenvalues of a reduced matrix (Eqs. (2.2)–(2.7)), which fixes the Riemann sheet of the fractional power unambiguously. The transition type is diagnosed from the volume dependence of Lee–Yang zeros on the complex β plane, extrapolated as β_0(V) = β_0^∞ + ζ/V over L_s = 4, 6, 8. The endpoint is identified as the μ at which the extrapolated Im(β_0^∞) crosses zero, giving μ_end = 0.375(20) in lattice units, and after scale setting T_E = 160 ± 3.5 MeV, μ_E = 725 ± 35 MeV (baryonic), with T_c = 172 ± 3 MeV at μ = 0.","tokens_in":9753,"tokens_out":11416,"duration_ms":247873,"significance":"This is the first ab initio lattice estimate of the QCD critical endpoint, and the methodology — transition-to-transition reweighting, determinant evaluation through the eigenvalues of the reduced matrix, and Lee–Yang finite-size scaling — is a genuine and reusable advance that later work in the field builds on. The result is falsifiable (the endpoint should move toward the μ = 0 axis as the light quark masses are reduced) and has direct bearing on heavy-ion searches for critical fluctuations. The paper is also commendably explicit about cost scaling toward physical masses and about the extrapolations still outstanding, and it states its limitations (finite volume, L_t = 4, heavy light quarks, R-algorithm step size) rather than hiding them.","major_comments":[{"comment":"The endpoint μ_end = 0.375(20) is read off a linear fit of Im(β_0^∞) against μ. The four fitted points (1.02, 1.12, 0.74, −0.25 at μ = 0.1, 0.2, 0.3, 0.4) are visibly non-monotonic: they rise from μ = 0.1 to 0.2 and then fall. A linear fit to non-monotonic data has a crossing that depends on the fit range and functional form; dropping the μ = 0.1 point or adding a quadratic term will move the crossing. The paper acknowledges the overshoot ('slightly overshoots') and cites the electroweak precedent, but does not demonstrate that the central value is stable. Please report μ_end for at least (i) the linear fit to all four points, (ii) a linear fit to μ = 0.2, 0.3, 0.4, and (iii) a quadratic fit, and state the expected critical scaling of Im(β_0^∞) near μ_E (the Lee–Yang zero vanishes with an exponent, not necessarily linearly) so the reader can judge whether the linear fit is a leading-order approximation. If the spread across these fits is within the quoted ±0.20, the result stands; if not, the error should be enlarged.","section":"§3, Figure 1 and Table 1","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The V → ∞ extrapolation β_0(V) = β_0^∞ + ζ/V rests on three volumes (L_s = 4, 6, 8). At μ = 0.1 the L_s = 6 value (2.66 ± 0.06) lies above the line through L_s = 4 (5.56 ± 0.08) and L_s = 8 (1.38 ± 0.06), so leading 1/V scaling is not validated at small μ; it is better near the endpoint only because the errors there are larger. Since the endpoint fit consumes these β_0^∞ values, the extrapolation systematic propagates directly into μ_end. Please show the effect of (i) fitting only L_s = 6 and 8, (ii) including a 1/V² term, and (iii) quoting χ²/dof for the three-point fits. In a paper whose central claim is a finite-size-scaling statement, the scaling ansatz should be tested rather than assumed.","section":"§3, Table 1","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The abstract quotes T_E = 160 ± 3.5 MeV, μ_E = 725 ± 35 MeV and T_c = 172 ± 3 MeV, but these errors appear to be statistical plus finite-volume only. The paper itself lists, in §4, the R-algorithm step-size extrapolation, the chiral extrapolation (m_π/m_ρ ≈ 0.73 versus the physical value, with m_{u,d} four times too heavy) and the continuum extrapolation (L_t = 4, O(a) staggered) as outstanding. In addition, the scale setting in §3 ('weighted average of R_0, m_ρ, √σ') is underspecified: as quoted in Table 1, the three quantities give lattice spacings that differ by up to ~17% at β = 5.208 (R_0 = 1.87, m_ρ = 1.22, √σ = 0.58 against 1/403, 770 and 440 MeV), and the reader cannot tell whether this spread enters the quoted errors. Please spell out the scale-setting procedure and state explicitly in the abstract that the quoted errors are statistical plus finite-volume and do not include the systematics listed in §4.","section":"§3 and §4, error budget","authors_acknowledge":null,"authors_acknowledge_p":null}],"minor_comments":[{"comment":"State the fit range and which μ points enter the dashed line, and label the fit form in the caption; as drawn, the reader cannot tell whether the line is a four-point or a two-point fit.","section":"Figure 1","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"Give the Re(β_0) → T mapping used to draw the crossover and first-order lines; the reader cannot reproduce the phase diagram from the text as written.","section":"Figure 2","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The β_0^∞ row is an extrapolation, not a measurement; label it as such and give the fit form and the volumes entering it.","section":"Table 1 caption","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The derivation is compressed. Add one line for the sign factor (−1)^{6L_s^3} in passing from det(P − e^{L_t μ}) to the product form of Eq. (2.7), and state explicitly that the eigenvalues of P are gauge invariant so the result does not depend on the partial gauge fixing.","section":"Eqs. (2.4)–(2.7)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The sentence 'no ab initio, lattice analysis based on QCD was done to locate the endpoint' should be softened to 'to our knowledge' and should cite the searches the authors are aware of, so the novelty claim is checkable.","section":"§1","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The phrase 'the former remains the same' has no clear antecedent; specify which cost is unchanged when going to physical masses.","section":"§3","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"Clarify the notation 'at least upto V = 4·12^3' — whether this means four spatial volumes of 12^3 or something else.","section":"§3","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The abstract's 'semi-realistic masses' would be more informative with the actual ratio, e.g. m_π/m_ρ ≈ 0.73 versus ≈ 0.18 in the real world, so the reader can judge how far the result is from the chiral limit.","section":"§1 and §3","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"Typographical: 'performes' (§1), 'three times larger then' (§3), 'upto' (§3), 'analyzes' (§2), and the mangled author affiliation 'E¨ otv¨ os' should be corrected.","section":"Throughout","authors_acknowledge":null,"authors_acknowledge_p":null}],"recommendation":"major_revision","confidential_remarks":"This is a landmark paper and the method is likely to be widely reused; the concern is not the soundness of the construction but that the headline errors in the abstract are smaller than the systematic uncertainties the paper itself enumerates in §4, and that the endpoint fit's stability under fit-form variation is not demonstrated. Both are fixable with additional analysis of data already in hand, and neither undermines the qualitative conclusion that an endpoint exists at large μ. The citation of the authors' own method paper [13] is appropriate and clearly flagged."},"author_rebuttal":null,"desk_editor":{"model":"selfhosted/deepseek-v4.1-flash","letter":"Worth your time, with a caveat about the error bar rather than the central value. This is the first lattice QCD estimate of the critical endpoint coordinates rather than a model guess, and the machinery is the interesting part: reweighting from mu=0 transition ensembles combined with the characteristic-polynomial determinant, det M = e^{-3 L^3 L_t mu} prod (e^{L_t mu} - lambda_i), which fixes the Riemann sheet of the fractional power unambiguously. That construction is clean, and it is what makes n_f=2+1 with a physical strange mass tractable here. The Lee-Yang zero analysis is a legitimate way to separate crossover from first order, and the electroweak precedent they lean on is real. Soft spots, in order of how much they matter. The endpoint: mu_end = 0.375(20) comes from a linear fit to Im(beta_inf) versus mu. At mu=0.4 the fit gives -0.25(10), a negative imaginary part of a Lee-Yang zero, which is unphysical. The authors say so (slightly overshoots) and cite the electroweak case, but they never show the crossing is stable under a curved fit. Near a critical point the zero should vanish as (mu_E - mu)^beta with beta not unity, so the linear crossing is a proxy. The quoted +/-0.20 is dominated by a systematic read off that same overshoot: the residual sets the error while the central value still comes from the fit that produced the residual. That is the one place I would push a referee to. The V to infinity extrapolation is the second: three volumes with a leading 1/V ansatz. At mu=0.1 the L_s=6 point sits well above the line through 4 and 8; it is cleaner near the endpoint where the errors are larger. Fine for exploratory work, not fine as a final number. Everything else is acknowledged: L_t=4, m_u,d four times heavy, no continuum or R-algorithm step-size extrapolation. The conclusions state all of this plainly, so the classifier note that no limitations are stated is wrong on the text. Who it is for: anyone on finite-density lattice QCD or the beam energy scan. The method is the durable contribution; the numbers have since moved. Peer review: yes, send it out. The method deserves scrutiny and the endpoint fit is a specific, answerable question for a referee.","headline":"First ab initio lattice estimate of the QCD critical endpoint, with a clean determinant construction; the endpoint fit and its error budget are the parts to press on.","tokens_in":10380,"tokens_out":1950,"would_cite":true,"duration_ms":39948,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"pith_extraction":{"msc":[],"pacs":["12.38.Gc","12.38.Mh","11.15.Ha","25.75.Nq"],"model":"selfhosted/deepseek-v4.1-flash","headline":"A lattice calculation places the QCD critical endpoint at $T_E = 160$ MeV and baryonic chemical potential $725$ MeV, by watching Lee–Yang zeros of the partition function close on the real axis.","keywords":["lattice QCD","finite temperature","finite baryon density","QCD critical endpoint","Lee-Yang zeros","reweighting","staggered fermions","quark-gluon plasma"],"falsifier":"A repeat of the analysis on larger spatial volumes, a finer lattice ($L_t = 6$ or $8$), or with lighter light quarks, in which the extrapolated imaginary part of the Lee–Yang zero does not reach zero at $T_{end} = 0.375(20)$ — or in which it does so at a substantially different $T$ — would show that the reported endpoint is an artifact of the three-volume $1/V$ fit or of the $L_t=4$ lattice spacing rather than a property of QCD.","tokens_in":10717,"feed_emoji":"⚛️","tokens_out":3250,"duration_ms":57406,"temperature":0.7,"pith_summary":"QCD is expected to have a critical point in the temperature–chemical-potential plane, where a line of first-order phase transitions ends and the smooth crossover seen at zero density begins; heavy-ion collisions passing near it would show characteristic non-monotonic fluctuations, but no first-principles lattice calculation had located it. This paper reports one. The authors build an ensemble of gauge configurations at zero chemical potential near the transition temperature, reweight them to non-zero $T$ and $T$ using the exact dependence of the Dirac determinant on $T$, and diagnose the transition from the volume scaling of Lee–Yang zeros of the partition function on the complex gauge-coupling plane. The extrapolated imaginary part of the zero shrinks as $T$ grows and is consistent with zero at $T_{end}=0.375(20)$ in lattice units, which the authors convert into $T_E = 160$ MeV and $T_E = 725$ MeV, together with $T_c = 172$ MeV at $T=0$. The calculation uses $n_f = 2+1$ staggered quarks with the strange mass near its physical value and the light quarks roughly four times too heavy, on $L_t = 4$ lattices.","feed_headline":"QCD's critical point pinned at 160 MeV and 725 MeV","feed_subtitle":"Reweighting zero-density lattices to finite density puts the endpoint of the first-order line within reach of a calculation.","key_machinery":"Three pieces carry the argument. First, a reweighting identity: the partition function at $(T, T)$ is written as an expectation value over an ensemble generated at $(T_w, T_w)$ with $T_w=0$, so that the ratio of bosonic actions and the ratio of determinant powers is measured configuration by configuration, with Ferrenberg–Swendsen reweighting in $T$. Second, an exact reduction of the fermion determinant: after gauge fixing to $A_0=0$ on all but the last timeslice, the determinant is manipulated into $T M = e^{-3L_s^3 L_t T} T (e^{L_t T} - T_i)$, the characteristic polynomial of a $6L_s^3$-dimensional matrix $T$ whose eigenvalues fix both the value of the determinant and the Riemann sheet of the fractional power in the $n_f/4$ exponent — the point that makes the complex-$T$ weight unambiguous. Third, the Lee–Yang zero analysis: zeros of the partition function in the complex $T$ plane are located on each volume, extrapolated as $T_0(V) = T_0^T + T/V$, and the vanishing or non-vanishing of the infinite-volume imaginary part distinguishes a first-order transition from a crossover.","core_discovery":"The paper claims the first ab initio lattice determination of the QCD critical endpoint. Working with $n_f=2+1$ dynamical staggered quarks at $m_s$ near its physical value and $m_{u,d}$ about four times heavier than in nature, on $L_t=4$ lattices with spatial sizes $L_s = 4, 6, 8$, the authors measure the complex Lee–Yang zeros of the partition function on the $T$ plane at several real chemical potentials. Extrapolating each zero to infinite volume via $T_0(V) = T_0^T + T/V$, they find that the imaginary part of the limiting zero decreases with $T$ and crosses zero at $T_{end} = 0.375(20)$ in lattice units, which they read as the disappearance of the crossover and the onset of a genuine first-order transition. Converting to physical units with a scale set by a weighted average of $R_0$, $m_$ and $T$, they report $T_E = 160$ MeV, $T_E = 725$ MeV for the baryonic chemical potential, and $T_c = 172$ MeV at vanishing $T$. The authors are explicit that this is an exploratory result: larger volumes, finer lattices and smaller quark masses are needed for a final answer, and they expect the endpoint to move closer to the $T=0$ axis once the light masses are reduced.","pith_inferences":["Because the light quark masses here are about four times physical, the reported $T_E$ is plausibly an upper bound: the authors themselves argue the endpoint moves toward the $T=0$ axis as $m_{u,d}$ decrease, so a physical-mass calculation would likely land below $725$ MeV.","The same machinery could be run at $L_t = 6$ or $8$ to test whether the endpoint survives continuum extrapolation; if $T_E$ drifts by more than the quoted few-percent error, the $L_t=4$ value is a lattice artifact rather than a QCD number.","The method's viability beyond $m_\\pi/2$ — the point where Glasgow-style reweighting fails — suggests the overlap problem is controlled by reweighting between transition configurations rather than between vacuum ones, a diagnostic other finite-density approaches could adopt.","A sharper test than the central values would be to check the predicted critical fluctuation signatures against a beam-energy scan whose freeze-out curve passes near $(T_E, T_E)$."],"forward_implications":["The QCD phase diagram acquires a concrete, non-perturbative anchor: a first-order line at large baryonic chemical potential terminating at $T_E \\approx 160$ MeV, $T_E \\approx 725$ MeV, with a crossover below it.","Heavy-ion programs can compare their collision trajectories against a calculated endpoint rather than a model estimate, since the endpoint's location follows from the QCD Lagrangian rather than from a chiral-model ansatz.","The reweighting-plus-eigenvalue technique extends to any number of staggered quarks and to finer lattices, where the eigenvalue cost scales as $L_s^9$ and stays subdominant to configuration generation.","The zero-density transition temperature $T_c = 172 \\pm 3$ MeV is fixed on the same lattices and with the same scale setting, giving an internally consistent baseline for the endpoint."],"supporting_citations":[{"why":"Supplies the finite-density reweighting method this paper generalizes from $n_f=4$ to arbitrary numbers of staggered quarks.","marker":"[13]"},{"why":"Ferrenberg–Swendsen reweighting, the technique used to scan in the gauge coupling $T$ after the determinant is computed.","marker":"[14]"},{"why":"Source of the idea for extracting the determinant's $T$-dependence from an eigenvalue problem rather than direct evaluation.","marker":"[18]"},{"why":"Yang–Lee theory of partition-function zeros, the basis for reading the transition order from the volume scaling of complex $T$ zeros.","marker":"[19]"},{"why":"Prior application of Lee–Yang zeros to locate an electroweak endpoint, the template for the $1/V$ extrapolation and its known overshoot behaviour.","marker":"[21]"},{"why":"Sommer scale $R_0$, one of the three quantities averaged to set the lattice spacing in physical units.","marker":"[16]"},{"why":"MILC public code providing the R-algorithm used to generate the gauge ensembles.","marker":"[22]"},{"why":"Model-based prediction of a critical endpoint on the $T$–$T$ plane, the expectation this lattice calculation is testing.","marker":"[3]"}],"fun_headline_variants":["Lattice estimate places QCD critical point at 160 MeV","QCD critical endpoint estimate lands at 160 MeV and 725 MeV","Exploratory lattice result puts QCD critical point at 160 MeV","Fourfold heavy light quarks keep QCD endpoint estimate exploratory","Lattice QCD critical point estimate is exploratory, authors caution"],"cache_read_input_tokens":0,"weakest_assumption_plain":"The endpoint is read off the zero crossing of a straight-line fit to the extrapolated imaginary part of the Lee–Yang zero as a function of chemical potential, using three volumes for the $1/V$ extrapolation and a fit whose own residual at the largest $T$ is negative and whose size is then used to set the systematic error.","fun_headline_variants_meta":{"raw":{"variants":["Lattice estimate places QCD critical point at 160 MeV","QCD critical endpoint estimate lands at 160 MeV and 725 MeV","Exploratory lattice result puts QCD critical point at 160 MeV","Fourfold heavy light quarks keep QCD endpoint estimate exploratory","Lattice QCD critical point estimate is exploratory, authors caution"]},"model":"selfhosted/deepseek-v4.1-flash","effort":"low","attempts":1,"cost_usd":0.0,"raw_usage":{"total_tokens":1867,"prompt_tokens":957,"completion_tokens":910,"prompt_tokens_details":null,"completion_tokens_details":{"reasoning_tokens":833}},"tokens_in":957,"tokens_out":910,"duration_ms":16779,"image_pages":[],"temperature":1.0,"reasoning_budget":50,"reasoning_tokens":833,"transport_provider":"selfhosted","cache_read_input_tokens":0,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-10-29T17:49:48.911344+00:00","model_set":{"reader":"selfhosted/deepseek-v4.1-flash"},"falsifier":"A repeat of the analysis on larger spatial volumes, a finer lattice ($L_t = 6$ or $8$), or with lighter light quarks, in which the extrapolated imaginary part of the Lee–Yang zero does not reach zero at $T_{end} = 0.375(20)$ — or in which it does so at a substantially different $T$ — would show that the reported endpoint is an artifact of the three-volume $1/V$ fit or of the $L_t=4$ lattice spacing rather than a property of QCD.","supporting_citations":[{"cited_title":"A new method to study lattice QCD at finite temperature and chemical potential","cited_arxiv_id":"hep-lat/0104001","evidence_quote":"Supplies the finite-density reweighting method this paper generalizes from $n_f=4$ to arbitrary numbers of staggered quarks."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Ferrenberg–Swendsen reweighting, the technique used to scan in the gauge coupling $T$ after the determinant is computed."},{"cited_title":"Toussaint, Nucl","cited_arxiv_id":null,"evidence_quote":"Source of the idea for extracting the determinant's $T$-dependence from an eigenvalue problem rather than direct evaluation."},{"cited_title":"Yang and T.D","cited_arxiv_id":null,"evidence_quote":"Yang–Lee theory of partition-function zeros, the basis for reading the transition order from the volume scaling of complex $T$ zeros."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Prior application of Lee–Yang zeros to locate an electroweak endpoint, the template for the $1/V$ extrapolation and its known overshoot behaviour."},{"cited_title":"Sommer, Nucl","cited_arxiv_id":null,"evidence_quote":"Sommer scale $R_0$, one of the three quantities averaged to set the lattice spacing in physical units."},{"cited_title":"See http://physics.indiana.edu/∼sg/milc.html","cited_arxiv_id":null,"evidence_quote":"MILC public code providing the R-algorithm used to generate the gauge ensembles."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Model-based prediction of a critical endpoint on the $T$–$T$ plane, the expectation this lattice calculation is testing."}],"review_version":1}