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Cited by 86High-Energy Particle Collisions ResearchQuantum Chromodynamics and Particle InteractionsParticle physics theoretical and experimental studies

Equation of state for two flavor QCD atNt=6

Open access
Bernard, Claude, Blum, Tom, DeTar, Carleton, Gottlieb, Steven, Rummukainen, Kari, Heller, Urs M., Hetrick, James E., Toussaint, Doug +3 more·1997·Physical Review D
DOI 10.1103/physrevd.55.6861
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Abstract

We calculate the two flavor equation of state for QCD on lattices with lattice spacing ${a=(6T)}^{\ensuremath{-}1}$ and find that cutoff effects are substantially reduced compared to an earlier study using ${a=(4T)}^{\ensuremath{-}1}$. However, it is likely that significant cutoff effects remain. We fit the lattice data to expected forms of the free energy density for a second order phase transition at zero-quark mass, which allows us to extrapolate the equation of state to ${m}_{q}=0$ and to extract the speed of sound. We find that the equation of state depends weakly on the quark mass for small quark mass.

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Crossref · 10.1103/physrevd.55.6861

Cites

27 of 27 references verified0 citation errors · 0 not checkable

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  • From the small values of surface tension and latent heat found in lattice QCD calculations, the amount of supercooling is found to be small.

    “From the small values of surface tension and latent heat found in lattice QCD calculations [82], the amount of supercooling is found to be small [85].”

    From Phase Transitions in the Early and Present Universe (2006) · cites this paper as [82]

    The citation [82] is attached to the claimed small lattice-QCD values of surface tension and latent heat; the separate citation [85] is attached to the supercooling conclusion. The cited paper’s Results and Analysis discusses energy density near the crossover, while its Conclusions say the simulations can say little about the nature of the transition. Searches for “surface tension” and “latent heat” found no passage reporting values for either quantity. (LLM, conf=0.76)

    Experimental — accuracy not yet measured

  • For the surface tension rather small values are found from quenched lattice QCD, σ ≈ 0.015 Tc^3.

    “For the surface tension rather small values are found from quenched lattice QCD, σ ≈ 0 . 015 T 3 c [78, 82].”

    From Phase Transitions in the Early and Present Universe (2006) · cites this paper as [82]

    The Results and Analysis and Conclusions sections discuss the two-flavor QCD equation of state, pressure, and energy density, but give no quenched-QCD surface-tension estimate. Searches for surface or interface tension and 0.015 found no passage supporting the quoted value. (LLM, conf=0.76)

    Experimental — accuracy not yet measured

  • For the values l = 1.4 Tc^4 and σ = 0.015 Tc^3 from quenched lattice QCD, A ≈ 3 × 10^-5; in the bag model A ≈ 5 × 10^-2 (σ/Tc^3)^3.

    “For the values of l = 1 . 4 T 4 c and σ = 0 . 015 T 3 c from quenched lattice QCD [82] A ≈ 3 × 10 -5 . In the bag model A ≈ 5 × 10 -2 ( σ/T 3 c ) 3 .”

    From Phase Transitions in the Early and Present Universe (2006) · cites this paper as [82]

    The citation is attached to the claimed quenched-lattice values of latent heat and surface tension. The Results and Analysis passage discusses energy density near a two-flavor QCD crossover, but gives neither l = 1.4 Tc^4 nor σ = 0.015 Tc^3. Searches for those values and for latent heat and surface tension found no supporting passage in our copy. (LLM, conf=0.76)

    Experimental — accuracy not yet measured

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Cites

Flagged first, then by citations

Research works printed but not linked: 20

  1. Preliminary results were reported in C. Bernard, T. Blum, C.E. DeTar, S. Gottlieb, U.M. Heller, J. E. Hetrick, L. Kärkkäinen, C. McNeile, K. Rummukainen, R. L. Sugar, D. Toussaint, M. Wingate, hep-lat/9608026, to be published in Nuc. Phys. B[Proc. Suppl.]. · arXiv
  2. T. Blum, S. Gottlieb, L. Kärkkäinen, and D. Toussaint, Nucl. Phys. B (Proc. Suppl.) 42, 460 (1995);
  3. S. Huang, J. Potvin, C. Rebbi and S. Sanielevici, Phys. Rev. D 42, 2864 (1990).
  4. J. Engels, J. Fingberg, F. Karsch, D. Miller and M. Weber, Phys. Lett. B 525, 625 (1990).
  5. S. Gottlieb, W. Liu, R. L. Renken, R. L. Sugar and D. Toussaint, Phys. Rev. D 35, 2531 (1987).
  6. The energy density in the SU(3) pure gauge case is also substantial below T c (F. Karsch, private communication). For the critical temperature of the SU(3) pure gauge transition see : G. Boyd, J. Engels, F. Karsch, E. Laermann, C. Legeland, M. Lüetgemeier, B. Petersson, Nucl. Phys. B469, 419 (1996). Lattice estimates of the mass of the lightest glueball have been given in G. Bali, K. Schilling, A. Hulsebos, A. Irving, C. Michael, and P. Stephenson, Phys. Lett. B 309, 378 (1993);
  7. H. Chen, J. Sexton, A. Vaccarino, and D. Weingarten, Nucl. Phys. B (Proc. Suppl.) 34, 357 (1994);
  8. K. Ra- jagopal, in Quark Gluon Plasma 2, R. Hwa, ed. (World Scientific, Singapore, 1995).
  9. P. Pfeuty and G. Toulouse, Introduction to the renor- malization group and its applications, (Wiley, New York, 1977).
  10. G. Baker, D. Meiron and B. Nickel, Phys. Rev. B 17, 1365 (1978);
  11. K. Kanaya and S. Kaya, Phys. Rev. D 51, 2404 (1995);
  12. P. Butera and M. Comi, Phys. Rev. B 52, 6185 (1995).
  13. F. Karsch and E. Laermann, Phys. Rev. D 50, 6954 (1994).
  14. F. Karsch, hep-lat/9503010, review talk from "Quark Matter 95"; · arXiv
  15. C. DeTar, Nucl. Phys. B (Proc. Suppl.) 42, 73 (1995);
  16. G. Boyd, J. Engels, F. Karsch, E. Laermann, C. Lege- land, M. Lütgemeier, and B. Petersson, Phys. Rev. Lett. 75, 4169 (1995).
  17. D. Toussaint, hep-lat/9607084, to be published in Phys. Rev. D. · arXiv
  18. Problems with O(4) scaling were reported by by A. Ukawa at the XIVth International Symposium on Lattice Field Theory, June 4-8th, 1996, St. Louis, to appear in Nucl. Phys. B (Proc.Suppl.), hep-lat/9612011; · arXiv
  19. G. Boyd reported similar findings by the Bielefeld group, "Two flavour QCD phase transition", hep-lat/9607046; We are cur- rently carrying out simulations at N t = 4 with am q = 0.008 -.025 on lattices with spatial sites 12 3 , 16 3 , and 24 3 . Our preliminary results are consistent with the above. · arXiv
  20. F. Karsch, B. Beinlich, J. Engels, R. Joswig, E. Laermann, A. Peikert, B. Petersson, "QCD Thermodynamics with Improved Actions", hep-lat/9608047. · arXiv

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Authors
Bernard, C., Blum, T., DeTar, C., Gottlieb, S., Rummukainen, K., Heller, U. M., Hetrick, J. E., Toussaint, D., Kärkkäinen, L., Sugar, R. L., & Wingate, M.
Affiliations
Washington University in St. Louis (US)
ORCID
Venue
Physical Review D
Publisher
American Physical Society (APS)
Published
1997-06-01
Volume
55
Issue
11
Pages
6861-6869
ISSN
  • 0556-2821 (ISSN-L)
  • 1089-4918
DOI
10.1103/physrevd.55.6861
OpenAlex
W3015683252
Cited by
86
References
27
Citations by year
2025: 1 · 2015: 1 · 2012: 2
FWCI
6.95
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • Scholarly Commons (University of the Pacific) (submittedVersion, cc-by)
  • CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
  • arXiv (Cornell University)
Funders
  • National Science Foundation
  • U.S. Department of Energy (FG02-85ER25000, FG0395ER40906, DE-AC02-)
Topics
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › High-Energy Particle Collisions Research
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Quantum Chromodynamics and Particle Interactions
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Particle physics theoretical and experimental studies
Keywords
two-flavor QCD, equation of state, lattice QCD, cutoff effects, sound velocity, chiral phase transition, free energy density, quark mass dependence

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