Pith. sign in

REVIEW 3 major objections 4 minor 4 cited by

Leading-Order QCD Equation of State in Strong Magnetic Fields at Nonzero Baryon Chemical Potential

T0 review · 3 major / 4 minor · reviewed 2026-08-05 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Strong magnetic fields reverse the temperature ordering of QCD's leading-order equation of state near the crossover, and can make the trace-anomaly coefficient negative.

desk verdict Solid extension of the magnetized QCD EoS program; the Theta2 sign change is real in the current data but numerically fragile and needs careful scrutiny before being used phenomenologically. read the letter →

arxiv 2508.07532 v1 pith:SWYIWJZQ submitted 2025-08-11 hep-lat hep-phnucl-th

Heng-Tong Ding , Jin-Biao Gu , Arpith Kumar , Sheng-Tai Li This is my paper
classification hep-lathep-phnucl-th PACS 12.38.Gc12.38.Mh
keywords latticeQCDequationofstatemagneticfieldbaryonchemicalpotentialTaylorexpansionconserved-chargefluctuationsstrangenessneutralityLandaulevels
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to establish that strong background magnetic fields qualitatively restructure the leading-order QCD equation of state at finite baryon chemical potential, in the temperature band just above the crossover. Using (2+1)-flavor lattice QCD with physical pion masses and continuum extrapolations from $N_\tau=8,12$, it computes the leading-order Taylor coefficients $q_1$, $s_1$, $P_2$, $N_1^{\mathrm{B}}$, $\Theta_2$, $\epsilon_2$, $\sigma_2$ for strangeness-neutral matter with charge-to-baryon ratio $r=0.4$. The central observations are temperature-band crossings in $q_1$ and $P_2$ at $eB\gtrsim0.6$ GeV$^2$, non-monotonic energy-like coefficients, and a possible sign change of the trace-anomaly coefficient $\Theta_2$ at strong fields and higher temperature, which would mean the pressure response dominates over the energy response. These coefficients are direct inputs for hydrodynamic modeling of heavy-ion collisions and for equations of state used in magnetar studies, and the paper provides analytic parametrizations for phenomenological use.

What carries the argument

The machinery is the Taylor expansion of the pressure in powers of $\hat\mu_B$ at fixed $eB$, with the chemical potential ratios $q_1\hat\mu_B$ and $s_1\hat\mu_B$ fixed by $\hat n_S=0$ and $\hat n_Q/\hat n_B=r$ using the second-order conserved-charge susceptibility matrix (Eqs. (31)-(32)). The leading-order coefficients are then $P_2=\frac12\hat\mu_B\hat n_{\mathrm{LO}}^{\mathrm{B}}(1+rq_1)$, $N_1^{\mathrm{B}}=\chi_2^B+q_1\chi_{11}^{BQ}+s_1\chi_{11}^{BS}$, and the energy-like coefficients $\Theta_2=-rT(\partial q_1/\partial T)N_1^{\mathrm{B}}+T(\partial P_2/\partial T)$, $\epsilon_2=\Theta_2+3P_2$, $\sigma_2=\epsilon_2+P_2-(1+rq_1)N_1^{\mathrm{B}}$. The physical driver invoked for the strong

What would settle it

A direct lattice check: compute $\Theta_2$ as $T\,\partial P_2/\partial T$ from the same ensembles (without the $q_1$ derivative term) and compare with the reported $\Theta_2$ at $eB\simeq0.8$ GeV$^2$, $T\simeq155$-$158$ MeV; if the simple derivative already reproduces the data, Eq. (64)'s extra term is not needed, and if it gives the opposite sign, the negative-trace-anomaly claim fails.

Watch

Extended reading notes

Core claim

The paper claims that, once strangeness neutrality and the isospin ratio $r=n_Q/n_B$ are imposed, the leading-order response of QCD matter to baryon chemical potential in a magnetic field is not a simple rescaling of the zero-field equation of state. From continuum-estimated second-order charge fluctuations it derives $q_1=(\mu_Q/\mu_B)_{\mathrm{LO}}$ and $s_1=(\mu_S/\mu_B)_{\mathrm{LO}}$, then the pressure coefficient $P_2$ and baryon-density coefficient $N_1^{\mathrm{B}}$. It finds that $-q_1$ grows with $eB$ by factors of about 3 at $eB\simeq0.15$ GeV$^2$ and up to about 11 at $eB\simeq0.8$ GeV$^2$, with the fixed-temperature bands crossing so that the low-temperature curve sits above the

Load-bearing premise

The sign change of the trace-anomaly coefficient rests on Eq. (64), which is stated without derivation and whose constraint-dependent term appears to have the wrong sign if the standard identity $\hat\Theta=T(\partial \hat p/\partial T)$ at fixed $\hat\mu_B$ is applied; if that term is wrong, the claimed $\Theta_2<0$ at strong fields and high $T$ does not follow.

Editorial extensions

If this is right

  • Heavy-ion phenomenological equations of state that use only the $\mu_B=0$ EoS plus a simple $eB$ rescaling will miss the hierarchy reversal: at $eB\gtrsim0.6$ GeV$^2$, the low-temperature pressure coefficient can exceed the high-temperature one, and $P_2$ develops a peak.
  • Strangeness-neutrality constraints suppress the magnetic enhancement of $P_2$ relative to the unconstrained $\hat\mu_Q=\hat\mu_S=0$ case; at $r=0$ the enhancement is the most muted even though $|q_1|$ is largest, so neutron-star-like modeling should not use the $\mu_Q=\mu_S=0$ pressure.
  • The ratio $N_1^{\mathrm{B}}/(2P_2)$ moves from about 1.02 toward 1.10 at strong fields, approaching the magnetized ideal-gas limit; the paper's analytic parametrization in Appendix B gives a direct way to implement this in models.
  • At strong fields, the trace-anomaly coefficient can be negative, meaning the pressure contribution dominates over the energy contribution ($3P_2>\epsilon_2$); if sustained, this changes expectations for hydrodynamic expansion and thermalization in magnetized matter.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper: if the sign in Eq. (64) is not correct, the negative-$\Theta_2$ conclusion is the first thing to fall; a direct lattice computation of $T\,\partial\hat p/\partial T$ at fixed $\hat\mu_B$ on the same ensembles would separate the two forms.
  • Beyond the paper: the temperature at which $P_2(T)$ peaks at large $eB$ could serve as a magnetic-field-dependent transition marker, but the 145-165 MeV window and present uncertainties leave that as a proposal, not a result of this paper.
  • Beyond the paper: the muted $P_2$ at $r=0$, if extended to cold $\beta$-equilibrated matter, would imply smaller magnetic corrections to neutron-star mass-radius relations than naive Landau-level estimates; the paper itself explicitly stops short of that cold extrapolation.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The manuscript presents a lattice QCD calculation of the leading-order Taylor coefficients of the QCD equation of state in a background magnetic field at nonzero baryon chemical potential. Using (2+1)-flavor HISQ configurations at physical quark masses with Nτ = 8 and 12, temperatures between 145 and 165 MeV, and eB up to 0.8 GeV², the authors combine previously published conserved-charge fluctuation results [106] with strangeness-neutrality and charge-to-baryon constraints to construct q1, s1, P2, N1^B, and the energy-like coefficients Θ2, ε2, and σ2. They report temperature-band crossings in q1 and P2, non-monotonic structures in the energy-like coefficients, and a possible sign change of Θ2 at strong fields and high temperature. The r-dependence and comparisons with HRG and ideal-gas models are also presented.

Significance. If the results are robust, this is the first continuum-estimated determination of these leading-order magnetized EoS coefficients at finite baryon density, and it provides useful benchmark data for heavy-ion and neutron-star applications. A clear strength is that the input susceptibilities come from independent lattice measurements rather than being fitted to the target coefficients, so the construction is not circular. The paper also provides compact parameterizations in Appendices B and C, which are practical for model comparisons. The central new physics claim — a field-induced restructuring of the temperature hierarchy and a possible negative trace-anomaly coefficient at strong fields — is interesting and falsifiable. However, the numerical support for the sign change of Θ2 needs strengthening before the claim can be regarded as established.

major comments (3)
  1. [Section VI D, Eq. (64)] Eq. (64) is stated without derivation, although every energy-like coefficient and the central sign-change claim rest on it. The formula is in fact correct: starting from Θ̂ = T ∂p̂/∂T at fixed μ̂s and using nQ = r nB and nS = 0, the total T-derivative of the constrained pressure expansion acquires the extra term −r T q1' N1^B μ̂B². But the manuscript should show this derivation explicitly rather than assert Eq. (64). Please add the derivation or provide a clear reference where it is carried out.
  2. [Section VI D, Figs. 8 and 9] The negative Θ2 at eB ≈ 0.79 GeV² and T ≳ 155 MeV is a delicate balance between T ∂P2/∂T and −r T q1' N1^B. These derivatives are obtained from 2D B-spline interpolation through only about five T values per lattice spacing and from a two-point linear 1/Nτ² extrapolation. The sign change sits near the upper end of the T window, where spline derivatives are least constrained. Please provide a systematic robustness check: vary spline order and knot placement, compare derivatives taken before versus after the continuum extrapolation, and, if possible, include Nτ = 16 data for P2 and q1 themselves. Without such a test, the sign change should be presented only as an unresolved possibility, not as a result.
  3. [Appendix A] The continuum extrapolation is linear in 1/Nτ² using only Nτ = 8 and 12. The text refers to Refs. [17,106] for an Nτ = 16 consistency check, but those references concern the second-order fluctuations and related quantities; the paper under review uses the derived coefficients P2, q1, and their T-derivatives appearing in Eq. (64). Please clarify the extent to which the Nτ = 16 validation covers these derived quantities, or state explicitly that the energy-like coefficients have only been computed at two lattice spacings. This matters because the claimed Θ2 behavior is a continuum-level claim.
minor comments (4)
  1. [Fig. 9 caption] The σ2 panel is described as the "bottom panel" but is actually the right panel of the figure; please correct the caption.
  2. [Appendix B, Eq. (B1)] The dimensionless variable denoted by a bar over T is not clearly defined in the equation; the text states T = 1 − Tpc/T, but the notation should be distinguished from the physical temperature T to avoid confusion.
  3. [Introduction and throughout] There are several typographical issues, e.g., "functional renormalizaiton group" in the Introduction and some broken math-mode spacing ("N f = 2 + 1 + 1"). A careful proofread is recommended.
  4. [Section VI D] The fixed temperatures T = 148, 155, 158 MeV used for the energy-like coefficients differ from the T = 145, 155, 165 MeV used elsewhere (Figs. 1, 4, 7). Please explain the choice or make the temperature sets consistent.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: all target coefficients are derived from independently measured susceptibilities; self-citations are data citations, not load-bearing conclusions.

full rationale

The paper's derivation chain is: (i) measure second-order conserved-charge susceptibilities on N_tau=8 and 12 lattices (input from companion paper [106]); (ii) solve the strangeness-neutrality and isospin constraints, Eqs. (29)-(30), for q1 and s1 via Eqs. (31)-(32); (iii) construct P2 and N1^B via Eqs. (60) and (62); (iv) construct Theta2, epsilon2 and sigma2 via Eqs. (64)-(66) from temperature derivatives of P2 and q1. None of the target quantities - the temperature-band crossings in q1 and P2, the non-monotonic structures, or the possible sign change of Theta2 - is used as a fit constraint or as an input to the susceptibility computation. The self-citations to [106] are citations to measured lattice data, not to conclusions of the present paper, and the N_tau=16 validation of the continuum extrapolation cited in [17,106] is independent supporting evidence. HRG and magnetized ideal-gas comparisons serve as external benchmarks. Equation (64) combines already-determined quantities; even if its sign or derivation were debatable, that is a correctness concern, not circularity. No step reduces by construction to its own output.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central results rest on second-order conserved-charge susceptibilities from the authors' companion paper [106], a linear 1/Nτ² continuum extrapolation using only Nτ=8 and 12, and leading-order truncation of the µ_B Taylor expansion. No new entities are introduced.

free parameters (3)
  • Rational polynomial fit coefficients for P2, -q1, s1 (T-parametrization) = Table II, entries ak, bk for eB in {0.0,0.1,0.2,0.4,0.6,0.79 GeV^2}
    Fitted to continuum-estimated lattice data; used to compute T derivatives entering Θ2, ε2, σ2.
  • Rational polynomial fit coefficients for P2, -q1, s1 (eB-parametrization) = Table III, entries ak, bk for T in {145,155,165 MeV}
    Fitted representation of eB dependence at fixed temperatures.
  • 2D B-spline interpolation in T-eB plane = Appendix A; spline bands from bootstrap
    Smoothing choice that sets crossing locations and derivative estimates for the continuum extrapolation.
assumptions (4)
  • domain assumption Linear continuum extrapolation in 1/Nτ² using Nτ=8 and 12 is valid for the derived coefficients
    Appendix A; validation with Nτ=16 is cited from Ref. [106] for susceptibilities, not for P2, Θ2, ε2, σ2.
  • domain assumption Leading-order Taylor expansion in µ_B is sufficient in the T and eB window studied
    Sec. II; higher order terms are neglected throughout.
  • domain assumption Strangeness neutrality and r=n_Q/n_B are imposed at leading order through linear q1 and s1
    Sec. II B, Eqs. 29-32; higher-order q3, s3 are dropped.
  • standard math Standard trace anomaly identity Θ̂ = T(∂p̂/∂T) at fixed µ̂_B
    Eq. 9; Eq. 64 appears to deviate from this identity.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Leading-Order QCD Equation of State in Strong Magnetic Fields at Nonzero Baryon Chemical Potential." pith.science (2026). https://pith.science/paper/SWYIWJZQ

@misc{pith2026250807532,
  author       = {Pith},
  title        = {Pith review of: Leading-Order QCD Equation of State in Strong Magnetic Fields at Nonzero Baryon Chemical Potential},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SWYIWJZQ}},
  note         = {Machine review of arXiv:2508.07532}
}
abstract

We present continuum-estimated $(2+1)$-flavor lattice QCD results for the leading-order Taylor expansion coefficients of the equation of state in strong magnetic fields and at nonzero baryon chemical potential. Simulations employ the highly improved staggered quark (HISQ) action with physical pion masses on lattices of temporal extent $N_\tau = 8,\,12$, covering $145 \lesssim T \lesssim 165~\mathrm{MeV}$ and $eB \lesssim 0.8~\mathrm{GeV}^2$, imposing strangeness neutrality with baseline results at electric charge to baryon number ratio $r = 0.4$. We determine the $T$--$eB$ dependence of $q_1$ and $s_1$ (electric charge and strangeness chemical potential ratios), pressure coefficient $P_2$, baryon number density coefficient $N_1^{\rm B}$, and energy-like coefficients $\Theta_2$ (trace anomaly), $\epsilon_2$ (energy density), and $\sigma_2$ (entropy density). Magnetic fields induce temperature-band crossings for $q_1$ and $P_2$ and non-monotonic structures in the energy-like coefficients, with $\Theta_2$ at strong fields possibly vanishing or turning negative at higher $T$, indicating dominance of the pressure term over the energy contribution. We also examine the $r$-dependence, finding that $r=0$ (charge-neutral matter) shows the most muted magnetic-field enhancement of $P_2$ despite larger $|q_1|$, providing a useful reference for neutron-star-like conditions. Comparisons with the hadron resonance gas (HRG) model show qualitative agreement at low $T$ and weak $eB$, with clear deviations near the crossover and at strong fields. These results provide useful input for constraining models and effective theories of QCD matter in strong magnetic fields at finite baryon density.

Figures

Figures reproduced from arXiv: 2508.07532 by the authors.

Figure 1
Figure 1. FIG. 1. Electric charge over baryon chemical potential leading-order coefficient, [PITH_FULL_IMAGE:figures/full_fig_p010_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Same as Fig. 1 but for strangeness over baryon chemical potential leading-order coefficient, [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Leading-order coefficient of the electric charge to [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Pressure leading-order Taylor expansion coefficient, [PITH_FULL_IMAGE:figures/full_fig_p014_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Isolated view of the right panel of Fig. 4 at fixed mag [PITH_FULL_IMAGE:figures/full_fig_p015_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Leading-order Taylor expansion coefficient of pressure [PITH_FULL_IMAGE:figures/full_fig_p016_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Leading-order Taylor expansion coefficients of baryon number density [PITH_FULL_IMAGE:figures/full_fig_p017_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Leading-order Taylor expansion coefficients of trace [PITH_FULL_IMAGE:figures/full_fig_p019_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Leading-order Taylor expansion coefficients of trace anomaly Θ [PITH_FULL_IMAGE:figures/full_fig_p020_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Leading-order Taylor expansion coefficients [PITH_FULL_IMAGE:figures/full_fig_p026_10.png]

Discussion (0). Sign in to comment.

Forward citations

Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Isospin-Driven Splitting of Chemical Potentials in Isobar Collisions from Lattice QCD

    hep-lat 2026-06 unverdicted novelty 6.0 of 10

    Lattice QCD yields first-principles splitting ratios for chemical potentials in Ru+Ru vs Zr+Zr collisions that are comparable in size to Bayesian STAR extractions, with Δμ_Q negative, Δμ_S positive, and only moderate ...

  2. Chiral first order phase transition at finite baryon density and zero temperature from self-consistent pole masses in the linear sigma model with quarks

    hep-ph 2026-04 unverdicted novelty 5.0 of 10

    In the two-flavor linear sigma model with quarks, the chiral phase transition at T=0 is first order and occurs at a quark chemical potential equal to the vacuum quark mass.

  3. Formation of Quark-Gluon Plasma droplets under Ultra-Relativistic Heavy Ion Collisions in the presence of magnetic fields with a modified hadronic medium

    hep-ph 2026-08 reject novelty 4.0 of 10

    Calculations of a droplet free-energy model indicate a kaonic-plus-pionic medium stabilizes QGP droplets more than pions alone, with chemical potential and magnetic field acting in opposition.

  4. Lattice QCD at finite temperature and density

    hep-lat 2026-03 unverdicted novelty 2.0 of 10

    A review of lattice QCD findings on the finite-temperature QCD transition at zero baryon chemical potential, its chiral limit behavior, constraints on the phase boundary and critical endpoint at finite density, plus a...

Reference graph

Works this paper leans on

127 extracted references · 7 canonical work pages · cited by 4 Pith papers

  1. [106]

    Ding, J.-B

    H.-T. Ding, J.-B. Gu, A. Kumar and S.-T. Li,Second order fluctuations of conserved charges in external magnetic fields,Phys. Rev. D111(2025) 114522 [2503.18467]

    arXiv 2025

  2. [1]

    Vachaspati,Magnetic fields from cosmological phase transitions,Phys

    T. Vachaspati,Magnetic fields from cosmological phase transitions,Phys. Lett. B265(1991) 258

    1991

  3. [2]

    Enqvist and P

    K. Enqvist and P. Olesen,On primordial magnetic fields of electroweak origin,Phys. Lett. B319(1993) 178 [hep-ph/9308270]

    arXiv 1993

  4. [3]

    Ichiki, K

    K. Ichiki, K. Takahashi, H. Ohno, H. Hanayama and N. Sugiyama,Cosmological Magnetic Field: a fossil of density perturbations in the early universe,Science 311(2006) 827 [astro-ph/0603631]

    arXiv 2006

  5. [4]

    Subramanian,The origin, evolution and signatures of primordial magnetic fields,Rept

    K. Subramanian,The origin, evolution and signatures of primordial magnetic fields,Rept. Prog. Phys.79 (2016) 076901 [1504.02311]

    arXiv 2016

  6. [5]

    Duncan and C

    R.C. Duncan and C. Thompson,Formation of very strongly magnetized neutron stars - implications for gamma-ray bursts,Astrophys. J. Lett.392(1992) L9

    1992

  7. [6]

    Harding and D

    A.K. Harding and D. Lai,Physics of Strongly Magnetized Neutron Stars,Rept. Prog. Phys.69(2006) 2631 [astro-ph/0606674]

    arXiv 2006

  8. [7]

    Skokov, A.Y

    V. Skokov, A.Y. Illarionov and V. Toneev,Estimate of the magnetic field strength in heavy-ion collisions,Int. J. Mod. Phys. A24(2009) 5925 [0907.1396]

    arXiv 2009

Show all 127 references
  1. [8]

    Deng and X.-G

    W.-T. Deng and X.-G. Huang,Event-by-event generation of electromagnetic fields in heavy-ion collisions,Phys. Rev. C85(2012) 044907 [1201.5108]

    2012 arXiv

  2. [9]

    Kharzeev, L.D

    D.E. Kharzeev, L.D. McLerran and H.J. Warringa, The Effects of topological charge change in heavy ion collisions: ’Event by event P and CP violation ’,Nucl. Phys. A803(2008) 227 [0711.0950]

    2008 arXiv

  3. [10]

    Fukushima, D.E

    K. Fukushima, D.E. Kharzeev and H.J. Warringa,The Chiral Magnetic Effect,Phys. Rev. D78(2008) 074033 [0808.3382]

    2008 arXiv

  4. [11]

    Kharzeev and J

    D.E. Kharzeev and J. Liao,Chiral magnetic effect reveals the topology of gauge fields in heavy-ion collisions,Nature Rev. Phys.3(2021) 55 [2102.06623]

    2021 arXiv

  5. [12]

    Fukushima, D.E

    K. Fukushima, D.E. Kharzeev and H.J. Warringa, Electric-current Susceptibility and the Chiral Magnetic Effect,Nucl. Phys. A836(2010) 311 [0912.2961]

    2010 arXiv

  6. [13]

    Fu,Fluctuations and correlations of hot QCD matter in an external magnetic field,Phys

    W.-j. Fu,Fluctuations and correlations of hot QCD matter in an external magnetic field,Phys. Rev. D88 (2013) 014009 [1306.5804]

    2013 arXiv

  7. [14]

    Fukushima and Y

    K. Fukushima and Y. Hidaka,Magnetic Shift of the Chemical Freeze-out and Electric Charge Fluctuations, Phys. Rev. Lett.117(2016) 102301 [1605.01912]. [15]STARcollaboration,Search for the chiral magnetic effect with isobar collisions at √sN N=200 GeV by the STAR Collaboration a...

    2016 arXiv

  8. [16]

    Kharzeev, J

    D.E. Kharzeev, J. Liao and S. Shi,Implications of the isobar-run results for the chiral magnetic effect in heavy-ion collisions,Phys. Rev. C106(2022) L051903 [2205.00120]

    2022 arXiv

  9. [17]

    Ding, J.-B

    H.-T. Ding, J.-B. Gu, A. Kumar, S.-T. Li and J.-H. Liu,Baryon Electric Charge Correlation as a Magnetometer of QCD,Phys. Rev. Lett.132(2024) 201903 [2312.08860]. [18]ALICEcollaboration,Measurement of correlations among net-charge, net-proton, and net-kaon multiplicity distribu...

    2024 arXiv

  10. [19]

    Endrodi,QCD with background electromagnetic fields on the lattice: A review,Prog

    G. Endrodi,QCD with background electromagnetic fields on the lattice: A review,Prog. Part. Nucl. Phys. 141(2025) 104153 [2406.19780]

    2025 arXiv

  11. [20]

    Adhikari et al.,Strongly interacting matter in extreme magnetic fields,2412.18632

    P. Adhikari et al.,Strongly interacting matter in extreme magnetic fields,2412.18632. 22

    arXiv

  12. [21]

    Mizher, M.N

    A.J. Mizher, M.N. Chernodub and E.S. Fraga,Phase diagram of hot QCD in an external magnetic field: possible splitting of deconfinement and chiral transitions,Phys. Rev. D82(2010) 105016 [1004.2712]

    2010 arXiv

  13. [22]

    Ferrari, A.F

    G.N. Ferrari, A.F. Garcia and M.B. Pinto,Chiral Transition Within Effective Quark Models Under Magnetic Fields,Phys. Rev. D86(2012) 096005 [1207.3714]

    2012 arXiv

  14. [23]

    Ayala, M

    A. Ayala, M. Loewe and R. Zamora,Inverse magnetic catalysis in the linear sigma model with quarks,Phys. Rev. D91(2015) 016002 [1406.7408]

    2015 arXiv

  15. [24]

    Tawfik and N

    A.N. Tawfik and N. Magdy,SU(3) Polyakov linear-σ model in an external magnetic field,Phys. Rev. C90 (2014) 015204 [1406.7488]

    2014 arXiv

  16. [25]

    Ayala, J.L

    A. Ayala, J.L. Hern´ andez, L.A. Hern´ andez, R.L.S. Farias and R. Zamora,Magnetic corrections to the boson self-coupling and boson-fermion coupling in the linear sigma model with quarks,Phys. Rev. D102 (2020) 114038 [2009.13740]

    2020 arXiv

  17. [26]

    Tawfik and A.M

    A.N. Tawfik and A.M. Diab,Chiral magnetic properties of QCD phase-diagram,Eur. Phys. J. A57 (2021) 200 [2106.04576]

    2021 arXiv

  18. [27]

    Ayala, R.L.S

    A. Ayala, R.L.S. Farias, L.A. Hern´ andez, A.J. Mizher, J. Rend´ on, C. Villavicencio et al.,Magnetic field dependence of the neutral pion longitudinal screening mass in the linear sigma model with quarks,Phys. Rev. D109(2024) 074019 [2311.13068]

    2024 arXiv

  19. [28]

    Fukushima, M

    K. Fukushima, M. Ruggieri and R. Gatto,Chiral magnetic effect in the PNJL model,Phys. Rev.D81 (2010) 114031 [1003.0047]

    2010 arXiv

  20. [29]

    Skokov,Phase diagram in an external magnetic field beyond a mean-field approximation,Phys

    V. Skokov,Phase diagram in an external magnetic field beyond a mean-field approximation,Phys. Rev. D 85(2012) 034026 [1112.5137]

    2012 arXiv

  21. [30]

    Miransky and I.A

    V.A. Miransky and I.A. Shovkovy,Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals, Phys. Rept.576(2015) 1 [1503.00732]

    2015 arXiv

  22. [31]

    Ayala, C.A

    A. Ayala, C.A. Dominguez, L.A. Hernandez, M. Loewe, A. Raya, J.C. Rojas et al.,Thermomagnetic properties of the strong coupling in the local Nambu–Jona-Lasinio model,Phys. Rev. D94(2016) 054019 [1603.00833]

    2016 arXiv

  23. [32]

    Farias, V.S

    R.L.S. Farias, V.S. Timoteo, S.S. Avancini, M.B. Pinto and G. Krein,Thermo-magnetic effects in quark matter: Nambu–Jona-Lasinio model constrained by lattice QCD,Eur. Phys. J. A53(2017) 101 [1603.03847]

    2017 arXiv

  24. [33]

    Cao,Recent progresses on QCD phases in a strong magnetic field: views from Nambu–Jona-Lasinio model,Eur

    G. Cao,Recent progresses on QCD phases in a strong magnetic field: views from Nambu–Jona-Lasinio model,Eur. Phys. J. A57(2021) 264 [2103.00456]

    2021 arXiv

  25. [34]

    Sheng, S.-Y

    X.-L. Sheng, S.-Y. Yang, Y.-L. Zou and D. Hou,Mass splitting and spin alignment forϕmesons in a magnetic field in NJL model,Eur. Phys. J. C84 (2024) 299 [2209.01872]

    2024 arXiv

  26. [35]

    Chahal, S

    N. Chahal, S. Dutt and A. Kumar,Effects of finite volume and magnetic fields on thermodynamic properties of quark matter and fluctuations of conserved charges,Phys. Rev. C107(2023) 045203 [2303.16840]

    2023 arXiv

  27. [36]

    Mao,Correlations and fluctuations in a magnetized PNJL model with and without the inverse magnetic catalysis effect*,Chin

    S. Mao,Correlations and fluctuations in a magnetized PNJL model with and without the inverse magnetic catalysis effect*,Chin. Phys. C49(2025) 063106 [2410.10217]

    2025 arXiv

  28. [37]

    Ali, C.A

    M.S. Ali, C.A. Islam and R. Sharma,QCD phase diagram in the T–eB plane for varying pion mass, Phys. Rev. D110(2024) 096011 [2407.14449]

    2024 arXiv

  29. [38]

    Kawaguchi, I

    M. Kawaguchi, I. Siddique and M. Huang,Effect of quark anomalous magnetic moment on neutral dense quark matter under magnetic field,Eur. Phys. J. C85 (2025) 246 [2408.14808]

    2025 arXiv

  30. [39]

    J. Mei, R. Wen, S. Mao, M. Huang and K. Xu, Magnetic catalysis and diamagnetism from pion fluctuations,Phys. Rev. D110(2024) 034024 [2402.19193]

    2024 arXiv

  31. [40]

    Mao and S

    S. Mao and S. Yang,Correlations and fluctuations in a magnetized three-flavor PNJL model with and without inverse magnetic catalysis effect,Phys. Rev. D112 (2025) 014026 [2504.14532]

    2025 arXiv

  32. [41]

    Endr¨ odi,QCD equation of state at nonzero magnetic fields in the Hadron Resonance Gas model, JHEP04(2013) 023 [1301.1307]

    G. Endr¨ odi,QCD equation of state at nonzero magnetic fields in the Hadron Resonance Gas model, JHEP04(2013) 023 [1301.1307]

    2013 arXiv

  33. [42]

    Bhattacharyya, S.K

    A. Bhattacharyya, S.K. Ghosh, R. Ray and S. Samanta,Exploring effects of magnetic field on the Hadron Resonance Gas,EPL115(2016) 62003 [1504.04533]

    2016 arXiv

  34. [43]

    Ferreira, P

    M. Ferreira, P. Costa and C. Providˆ encia,Net baryon-number fluctuations in magnetized quark matter,Phys. Rev. D98(2018) 034003 [1806.05758]

    2018 arXiv

  35. [44]

    Kadam, S

    G. Kadam, S. Pal and A. Bhattacharyya,Interacting hadron resonance gas model in magnetic field and the fluctuations of conserved charges,J. Phys. G47 (2020) 125106 [1908.10618]

    2020 arXiv

  36. [45]

    Marczenko, M

    M. Marczenko, M. Szyma´ nski, P.M. Lo, B. Karmakar, P. Huovinen, C. Sasaki et al.,Magnetic effects in the hadron resonance gas,Phys. Rev. C110(2024) 065203 [2405.15745]

    2024 arXiv

  37. [46]

    Vovchenko,Magnetic field effect on hadron yield ratios and fluctuations in a hadron resonance gas, Phys

    V. Vovchenko,Magnetic field effect on hadron yield ratios and fluctuations in a hadron resonance gas, Phys. Rev. C110(2024) 034914 [2405.16306]

    2024 arXiv

  38. [47]

    Samanta and W

    R. Samanta and W. Broniowski,Magnetic properties of the hadron resonance gas with physical magnetic moments,2505.14484

  39. [48]

    Blaizot, E.S

    J.-P. Blaizot, E.S. Fraga and L.F. Palhares,Effect of quark masses on the QCD pressure in a strong magnetic background,Phys. Lett. B722(2013) 167 [1211.6412]

    2013 arXiv

  40. [49]

    Karmakar, N

    B. Karmakar, N. Haque and M.G. Mustafa, Second-order quark number susceptibility of deconfined QCD matter in the presence of a magnetic field,Phys. Rev. D102(2020) 054004 [2003.11247]

    2020 arXiv

  41. [50]

    Fraga, L.F

    E.S. Fraga, L.F. Palhares and T.E. Restrepo,Cold and dense perturbative QCD in a very strong magnetic background,Phys. Rev. D109(2024) 054033 [2312.13952]

    2024 arXiv

  42. [51]

    Fraga, L.F

    E.S. Fraga, L.F. Palhares and T.E. Restrepo, Susceptibilities and Taylor coefficients of magnetic QCD from perturbation theory,2507.14360

  43. [52]

    Rebhan, A

    A. Rebhan, A. Schmitt and S.A. Stricker,Anomalies and the chiral magnetic effect in the Sakai-Sugimoto model,JHEP01(2010) 026 [0909.4782]

    2010 arXiv

  44. [53]

    Preis, A

    F. Preis, A. Rebhan and A. Schmitt,Inverse magnetic catalysis in dense holographic matter,JHEP03(2011) 033 [1012.4785]

    2011 arXiv

  45. [54]

    Fukushima and P

    K. Fukushima and P. Morales,Spatial modulation and topological current in holographic QCD matter,Phys. Rev. Lett.111(2013) 051601 [1305.4115]. 23

    2013 arXiv

  46. [55]

    Dudal and T.G

    D. Dudal and T.G. Mertens,Holographic estimate of heavy quark diffusion in a magnetic field,Phys. Rev. D 97(2018) 054035 [1802.02805]

    2018 arXiv

  47. [56]

    Fukushima and A

    K. Fukushima and A. Okutsu,Electric conductivity with the magnetic field and the chiral anomaly in a holographic QCD model,Phys. Rev. D105(2022) 054016 [2106.07968]

    2022 arXiv

  48. [57]

    Zhu and D

    Z.-R. Zhu and D. Hou,Inverse magnetic catalysis and energy loss in a holographic QCD model,Phys. Rev. D 110(2024) 066010 [2305.12375]

    2024 arXiv

  49. [58]

    Critelli, S.I

    R. Critelli, S.I. Finazzo, M. Zaniboni and J. Noronha, Anisotropic shear viscosity of a strongly coupled non-Abelian plasma from magnetic branes,Phys. Rev. D90(2014) 066006 [1406.6019]

    2014 arXiv

  50. [59]

    Dudal and T.G

    D. Dudal and T.G. Mertens,Melting of charmonium in a magnetic field from an effective AdS/QCD model, Phys. Rev. D91(2015) 086002 [1410.3297]

    2015 arXiv

  51. [60]

    L. Yin, D. Hou and H.-c. Ren,Chiral magnetic effect and three-point function from AdS/CFT correspondence,JHEP09(2021) 117 [2102.04851]

    2021 arXiv

  52. [61]

    L. Zhu, Z. Gao, W. Ke and H. Zhang,Bayesian inference of the magnetic field and chemical potential on holographic jet quenching in heavy-ion collisions, 2506.00340

  53. [62]

    R. Wen, C. Huang and M. Huang,Functional renormalization group study of anomalous magnetic moment in a low energy effective theory,2506.20246

    arXiv

  54. [63]

    R. Wen, S. Yin, W.-j. Fu and M. Huang,Functional renormalization group study of neutral and charged pions in magnetic fields in the quark-meson model, Phys. Rev. D108(2023) 076020 [2306.04045]

    2023 arXiv

  55. [64]

    Mueller and J.M

    N. Mueller and J.M. Pawlowski,Magnetic catalysis and inverse magnetic catalysis in QCD,Phys. Rev. D 91(2015) 116010 [1502.08011]

    2015 arXiv

  56. [65]

    Cea and L

    P. Cea and L. Cosmai,Abelian chromomagnetic fields and confinement,JHEP02(2003) 031 [hep-lat/0204023]

    2003 arXiv

  57. [66]

    D’Elia, S

    M. D’Elia, S. Mukherjee and F. Sanfilippo,QCD Phase Transition in a Strong Magnetic Background, Phys. Rev. D82(2010) 051501 [1005.5365]

    2010 arXiv

  58. [67]

    G.S. Bali, F. Bruckmann, G. Endr¨ odi, S.D. Katz and A. Sch¨ afer,The QCD equation of state in background magnetic fields,JHEP08(2014) 177 [1406.0269]

    2014 arXiv

  59. [68]

    G.S. Bali, F. Bruckmann, G. Endrodi, Z. Fodor, S.D. Katz, S. Krieg et al.,The QCD phase diagram for external magnetic fields,JHEP02(2012) 044 [1111.4956]

    2012 arXiv

  60. [69]

    Braguta, M.N

    V.V. Braguta, M.N. Chernodub, A.Y. Kotov, A.V. Molochkov and A.A. Nikolaev,Finite-density QCD transition in a magnetic background field,Phys. Rev. D100(2019) 114503 [1909.09547]

    2019 arXiv

  61. [70]

    D’Elia, L

    M. D’Elia, L. Maio, F. Sanfilippo and A. Stanzione, Phase diagram of QCD in a magnetic background, Phys. Rev. D105(2022) 034511 [2111.11237]

    2022 arXiv

  62. [71]

    H.-T. Ding, C. Schmidt, A. Tomiya and X.-D. Wang, Chiral phase structure of three flavor QCD in a background magnetic field,Phys. Rev. D102(2020) 054505 [2006.13422]

    2020 arXiv

  63. [72]

    D’Elia, L

    M. D’Elia, L. Maio, K. Zambello and G. Zanichelli, Roberge-Weiss transition for QCD in a magnetic background,Phys. Rev. D111(2025) 094509 [2502.19294]

    2025 arXiv

  64. [73]

    Astrakhantsev, V.V

    N. Astrakhantsev, V.V. Braguta, M. D’Elia, A.Y. Kotov, A.A. Nikolaev and F. Sanfilippo,Lattice study of the electromagnetic conductivity of the quark-gluon plasma in an external magnetic field, Phys. Rev. D102(2020) 054516 [1910.08516]

    2020 arXiv

  65. [74]

    Velasco, B.B

    E.G. Velasco, B.B. Brandt, F. Cuteri, G. Endr˝ odi and G. Mark´ o,Anomalous transport phenomena on the lattice,PoSLA TTICE2022(2023) 173 [2212.02148]

    2023 arXiv

  66. [75]

    Almirante, N

    G. Almirante, N. Astrakhantsev, V.V. Braguta, M. D’Elia, L. Maio, M. Naviglio et al.,Electrical conductivity of the quark-gluon plasma in the presence of strong magnetic fields,Phys. Rev. D111(2025) 034505 [2406.18504]

    2025 arXiv

  67. [76]

    Brandt, G

    B.B. Brandt, G. Endr˝ odi, E. Garnacho-Velasco, G. Mark´ o and A.D.M. Valois,Localized Chiral Magnetic Effect in equilibrium QCD,2409.17616

  68. [77]

    Bonati, M

    C. Bonati, M. D’Elia and A. Rucci,Heavy quarkonia in strong magnetic fields,Phys. Rev. D92(2015) 054014 [1506.07890]

    2015 arXiv

  69. [78]

    Endr˝ odi and G

    G. Endr˝ odi and G. Mark´ o,Magnetized baryons and the QCD phase diagram: NJL model meets the lattice, JHEP08(2019) 036 [1905.02103]

    2019 arXiv

  70. [79]

    Ding, S.T

    H.T. Ding, S.T. Li, J.H. Liu and X.D. Wang,Chiral condensates and screening masses of neutral pseudoscalar mesons in thermomagnetic QCD medium, Phys. Rev. D105(2022) 034514 [2201.02349]

    2022 arXiv

  71. [80]

    Ding, J.-B

    H.-T. Ding, J.-B. Gu, S.-T. Li and R. Thakkar,Chiral condensates and screening masses of neutral pseudoscalar mesons from lattice QCD at physical quark masses,Phys. Rev. D111(2025) 074513 [2501.11262]

    2025 arXiv

  72. [81]

    G.S. Bali, F. Bruckmann, G. Endrodi, Z. Fodor, S.D. Katz and A. Schafer,QCD quark condensate in external magnetic fields,Phys. Rev. D86(2012) 071502 [1206.4205]

    2012 arXiv

  73. [82]

    Bruckmann, G

    F. Bruckmann, G. Endrodi and T.G. Kovacs,Inverse magnetic catalysis and the Polyakov loop,JHEP04 (2013) 112 [1303.3972]

    2013 arXiv

  74. [83]

    G.S. Bali, F. Bruckmann, G. Endrodi, F. Gruber and A. Schaefer,Magnetic field-induced gluonic (inverse) catalysis and pressure (an)isotropy in QCD,JHEP04 (2013) 130 [1303.1328]

    2013 arXiv

  75. [84]

    Bonati, M

    C. Bonati, M. D’Elia, M. Mariti, M. Mesiti, F. Negro, A. Rucci et al.,Magnetic field effects on the static quark potential at zero and finite temperature,Phys. Rev. D94(2016) 094007 [1607.08160]

    2016 arXiv

  76. [85]

    D’Elia, F

    M. D’Elia, F. Manigrasso, F. Negro and F. Sanfilippo, QCD phase diagram in a magnetic background for different values of the pion mass,Phys. Rev. D98 (2018) 054509 [1808.07008]

    2018 arXiv

  77. [86]

    Endrodi, M

    G. Endrodi, M. Giordano, S.D. Katz, T.G. Kov´ acs and F. Pittler,Magnetic catalysis and inverse catalysis for heavy pions,JHEP07(2019) 007 [1904.10296]

    2019 arXiv

  78. [87]

    Brandt, F

    B.B. Brandt, F. Cuteri, G. Endr˝ odi, G. Mark´ o, L. Sandbote and A.D.M. Valois,Thermal QCD in a non-uniform magnetic background,JHEP11(2023) 229 [2305.19029]

    2023 arXiv

  79. [88]

    D’Elia and F

    M. D’Elia and F. Negro,Chiral Properties of Strong Interactions in a Magnetic Background,Phys. Rev. D 83(2011) 114028 [1103.2080]

    2011 arXiv

  80. [89]

    Ding, S.T

    H.T. Ding, S.T. Li, A. Tomiya, X.D. Wang and Y. Zhang,Chiral properties of (2+1)-flavor QCD in strong magnetic fields at zero temperature,Phys. Rev. D104(2021) 014505 [2008.00493]

    2021 arXiv

  81. [90]

    Allton, S

    C.R. Allton, S. Ejiri, S.J. Hands, O. Kaczmarek, F. Karsch, E. Laermann et al.,The QCD thermal 24 phase transition in the presence of a small chemical potential,Phys. Rev. D66(2002) 074507 [hep-lat/0204010]

    2002 arXiv

  82. [91]

    Gavai and S

    R.V. Gavai and S. Gupta,Pressure and nonlinear susceptibilities in QCD at finite chemical potentials, Phys. Rev. D68(2003) 034506 [hep-lat/0303013]. [92]HotQCDcollaboration,Fluctuations and Correlations of net baryon number, electric charge, and strangeness: A comparison of la...

    2003 arXiv

  83. [93]

    Bazavov et al.,Skewness, kurtosis, and the fifth and sixth order cumulants of net baryon-number distributions from lattice QCD confront high-statistics STAR data,Phys

    A. Bazavov et al.,Skewness, kurtosis, and the fifth and sixth order cumulants of net baryon-number distributions from lattice QCD confront high-statistics STAR data,Phys. Rev. D101(2020) 074502 [2001.08530]. [94]HotQCDcollaboration,Second order cumulants of conserved charge fl...

    2020 arXiv

  84. [95]

    Bazavov et al.,The QCD Equation of State to O(µ6 B)from Lattice QCD,Phys

    A. Bazavov et al.,The QCD Equation of State to O(µ6 B)from Lattice QCD,Phys. Rev. D95(2017) 054504 [1701.04325]. [96]HotQCDcollaboration,Equation of state and speed of sound of (2+1)-flavor QCD in strangeness-neutral matter at nonvanishing net baryon-number density, Phys. Rev....

    2017 arXiv

  85. [97]

    Roberge and N

    A. Roberge and N. Weiss,Gauge Theories With Imaginary Chemical Potential and the Phases of QCD, Nucl. Phys. B275(1986) 734

    1986

  86. [98]

    de Forcrand and O

    P. de Forcrand and O. Philipsen,The QCD phase diagram for small densities from imaginary chemical potential,Nucl. Phys. B642(2002) 290 [hep-lat/0205016]

    2002 arXiv

  87. [99]

    D’Elia and M.-P

    M. D’Elia and M.-P. Lombardo,Finite density QCD via imaginary chemical potential,Phys. Rev. D67 (2003) 014505 [hep-lat/0209146]

    2003 arXiv

  88. [100]

    Clarke, P

    D.A. Clarke, P. Dimopoulos, F. Di Renzo, J. Goswami, C. Schmidt, S. Singh et al.,Searching for the QCD critical endpoint using multi-point Pad´ e approximations,2405.10196

    arXiv

  89. [101]

    A. Adam, S. Bors´ anyi, Z. Fodor, J.N. Guenther, P. Kumar, P. Parotto et al.,High-precision baryon number cumulants from lattice QCD in a finite box: cumulant ratios, Lee-Yang zeros and critical endpoint predictions,2507.13254

    arXiv

  90. [102]

    D’Elia, G

    M. D’Elia, G. Gagliardi and F. Sanfilippo,Higher order quark number fluctuations via imaginary chemical potentials inN f = 2 + 1QCD,Phys. Rev. D 95(2017) 094503 [1611.08285]

    2017 arXiv

  91. [103]

    Ding, S.T

    H.T. Ding, S.T. Li, Q. Shi and X.D. Wang, Fluctuations and correlations of net baryon number, electric charge and strangeness in a background magnetic field,Eur. Phys. J. A57(2021) 202 [2104.06843]

    2021 arXiv

  92. [104]

    Ding, S.-T

    H.-T. Ding, S.-T. Li, J.-H. Liu and X.-D. Wang, Fluctuations of Conserved Charges in Strong Magnetic Fields from Lattice QCD,Acta Phys. Polon. Supp.16 (2023) 1 [2208.07285]

    2023 arXiv

  93. [105]

    Ding, J.-B

    H.-T. Ding, J.-B. Gu, A. Kumar, S.-T. Li and J.-H. Liu,Baryon-Electric Charge Correlations and Chemical Potentials as Probes of Magnetized QCD, PoSLA TTICE2024(2025) 191 [2502.02956]

    2025 arXiv

  94. [107]

    Pandav, D

    A. Pandav, D. Mallick and B. Mohanty,Search for the QCD critical point in high energy nuclear collisions, Prog. Part. Nucl. Phys.125(2022) 103960 [2203.07817]

    2022 arXiv

  95. [108]

    Nonaka,Experimental Overview on Fluctuations of Conserved Charges,Acta Phys

    T. Nonaka,Experimental Overview on Fluctuations of Conserved Charges,Acta Phys. Polon. Supp.16(2023) 1

    2023

  96. [109]

    Borsanyi, B

    S. Borsanyi, B. Brandt, G. Endrodi, J. N. Guenther, R. Kara and A.D. Marques Valois,QCD equation of state in the presence of magnetic fields at low density, PoSLA TTICE2023(2024) 164 [2312.15118]

    2024 arXiv

  97. [111]

    Marques Valois, S

    A.D. Marques Valois, S. Borsanyi, B. Brandt, G. Endrodi, J.N. Guenther, M.-A. Petri et al.,Dense and magnetized QCD from imaginary chemical potential,PoSLA TTICE2024(2025) 177 [2502.01132]

    2025 arXiv

  98. [112]

    Astrakhantsev, V.V

    N. Astrakhantsev, V.V. Braguta, A.Y. Kotov and A.A. Roenko,QCD equation of state at nonzero baryon density in an external magnetic field,Phys. Rev. D109(2024) 094511 [2403.07783]

    2024 arXiv

  99. [113]

    Bazavov et al.,Freeze-out Conditions in Heavy Ion Collisions from QCD Thermodynamics,Phys

    A. Bazavov et al.,Freeze-out Conditions in Heavy Ion Collisions from QCD Thermodynamics,Phys. Rev. Lett.109(2012) 192302 [1208.1220]

    2012 arXiv

  100. [114]

    Bazavov et al.,Additional Strange Hadrons from QCD Thermodynamics and Strangeness Freezeout in Heavy Ion Collisions,Phys

    A. Bazavov et al.,Additional Strange Hadrons from QCD Thermodynamics and Strangeness Freezeout in Heavy Ion Collisions,Phys. Rev. Lett.113(2014) 072001 [1404.6511]

    2014 arXiv

  101. [115]

    G.S. Bali, G. Endr˝ odi and S. Piemonte,Magnetic susceptibility of QCD matter and its decomposition from the lattice,JHEP07(2020) 183 [2004.08778]

    2020 arXiv

  102. [116]

    Karsch, K

    F. Karsch, K. Redlich and A. Tawfik,Thermodynamics at nonzero baryon number density: A Comparison of lattice and hadron resonance gas model calculations, Phys. Lett. B571(2003) 67 [hep-ph/0306208]

    2003 arXiv

  103. [117]

    Andronic, P

    A. Andronic, P. Braun-Munzinger and J. Stachel, Hadron production in central nucleus-nucleus collisions at chemical freeze-out,Nucl. Phys. A772(2006) 167 [nucl-th/0511071]

    2006 arXiv

  104. [118]

    Huovinen and P

    P. Huovinen and P. Petreczky,QCD Equation of State and Hadron Resonance Gas,Nucl. Phys. A837(2010) 26 [0912.2541]

    2010 arXiv

  105. [119]

    Vovchenko and H

    V. Vovchenko and H. Stoecker,Examination of the sensitivity of the thermal fits to heavy-ion hadron yield data to the modeling of the eigenvolume interactions, Phys. Rev. C95(2017) 044904 [1606.06218]

    2017 arXiv

  106. [120]

    Hagedorn,Statistical thermodynamics of strong interactions at high-energies,Nuovo Cim

    R. Hagedorn,Statistical thermodynamics of strong interactions at high-energies,Nuovo Cim. Suppl.3 (1965) 147. [121]Particle Data Groupcollaboration,Review of Particle Physics,PTEP2020(2020) 083C01

    1965

  107. [122]

    Alba et al.,Constraining the hadronic spectrum through QCD thermodynamics on the lattice,Phys

    P. Alba et al.,Constraining the hadronic spectrum through QCD thermodynamics on the lattice,Phys. Rev. D96(2017) 034517 [1702.01113]

    2017 arXiv

  108. [123]

    Karsch, K

    F. Karsch, K. Morita and K. Redlich,Effects of kinematic cuts on net-electric charge fluctuations, 25 Phys. Rev. C93(2016) 034907 [1508.02614]

    2016 arXiv

  109. [124]

    Bellwied, S

    R. Bellwied, S. Borsanyi, Z. Fodor, J.N. Guenther, J. Noronha-Hostler, P. Parotto et al.,Off-diagonal correlators of conserved charges from lattice QCD and how to relate them to experiment,Phys. Rev. D101 (2020) 034506 [1910.14592]

    2020 arXiv

  110. [125]

    Kapusta and C

    J.I. Kapusta and C. Gale,Finite-temperature field theory: Principles and applications, Cambridge Monographs on Mathematical Physics, Cambridge University Press (2011), 10.1017/CBO9780511535130

    2011 doi

  111. [126]

    Laine and A

    M. Laine and A. Vuorinen,Basics of Thermal Field Theory, vol. 925, Springer (2016), 10.1007/978-3-319-31933-9, [1701.01554]. [127]HPQCD, UKQCDcollaboration,Highly improved staggered quarks on the lattice, with applications to charm physics,Phys. Rev. D75(2007) 054502 [hep-lat/0610092]

    2016 arXiv

  112. [128]

    Bazavov et al.,Meson screening masses in (2+1)-flavor QCD,Phys

    A. Bazavov et al.,Meson screening masses in (2+1)-flavor QCD,Phys. Rev. D100(2019) 094510 [1908.09552]. [129]HotQCDcollaboration,Taylor expansions and Pad´ e approximants for cumulants of conserved charge fluctuations at nonvanishing chemical potentials,Phys. Rev. D105(2022) 0...

    2019 arXiv

  113. [129]

    = 155.029 MeV, is determined from the peak of the chiral susceptibility [106]. eB-parametrization: Following a similar procedure as above, we consider the parametrization ofO(eB) with re- spect to magnetic field strengtheB, evaluated at several fixed temperatures,T∈ {145,155,1...

    1954

  114. [130]

    Bollweg, H.T

    D. Bollweg, H.T. Ding, J. Goswami, F. Karsch, S. Mukherjee, P. Petreczky et al., Strangeness-correlations on the pseudocritical line in (2+1)-flavor QCD,Phys. Rev. D110(2024) 054519 [2407.09335]

    2024 arXiv

  115. [131]

    Al-Hashimi and U.J

    M.H. Al-Hashimi and U.J. Wiese,Discrete Accidental Symmetry for a Particle in a Constant Magnetic Field on a Torus,Annals Phys.324(2009) 343 [0807.0630]

    2009 arXiv

  116. [132]

    ’t Hooft,A Property of Electric and Magnetic Flux in Nonabelian Gauge Theories,Nucl

    G. ’t Hooft,A Property of Electric and Magnetic Flux in Nonabelian Gauge Theories,Nucl. Phys. B153 (1979) 141. [133]HotQCDcollaboration,SIMULATeQCD: A simple multi-GPU lattice code for QCD calculations,Comput. Phys. Commun.300(2024) 109164 [2306.01098]

    1979 arXiv

  117. [134]

    D’Elia, L

    M. D’Elia, L. Maio, F. Sanfilippo and A. Stanzione, Confining and chiral properties of QCD in extremely strong magnetic fields,Phys. Rev. D104(2021) 114512 [2109.07456]

    2021 arXiv

  118. [135]

    Gusynin, V.A

    V.P. Gusynin, V.A. Miransky and I.A. Shovkovy, Catalysis of dynamical flavor symmetry breaking by a magnetic field in (2+1)-dimensions,Phys. Rev. Lett. 73(1994) 3499 [hep-ph/9405262]

    1994 arXiv

  119. [136]

    Gusynin, V.A

    V.P. Gusynin, V.A. Miransky and I.A. Shovkovy, Dimensional reduction and catalysis of dynamical symmetry breaking by a magnetic field,Nucl. Phys. B 462(1996) 249 [hep-ph/9509320]. [137]HotQCDcollaboration,Equation of state in ( 2+1 )-flavor QCD,Phys. Rev. D90(2014) 094503 [140...

    1996 arXiv

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.