Remarks on the chiral phase transition in chromodynamics
Abstract
The phase transition restoring chiral symmetry at finite temperatures is considered in a linear $\ensuremath{\sigma}$ model. For three or more massless flavors, the perturbative $\ensuremath{\epsilon}$ expansion predicts the phase transition is of first order. At high temperatures, the ${\mathrm{U}}_{A}(1)$ symmetry will also be effectively restored.
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A self-consistent calculation of the surface tension within the bag model shows that the surface tension vanishes for massless quarks and gluons if no interactions besides the bag constant are taken into account.
“A self-consistent calculation of the surface tension within the bag model shows that the surface tension vanishes for massless quarks and gluons if no interactions besides the bag constant (i.e. α s = 0) are taken into account [79].”
From Phase Transitions in the Early and Present Universe (2006) · cites this paper as [79]
Cites
Symmetry Breaking through Bell-Jackiw Anomalies
't Hooft, G. (1976) · Physical Review Letters · doi:10.1103/physrevlett.37.8 · Cited by 3,362 · see citing works
Computation of the quantum effects due to a four-dimensional pseudoparticle
Hooft, G. ’. (1976) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.14.3432 · Cited by 2,906 · see citing works
QCD and instantons at finite temperature
Gross, D. J., Pisarski, R. D., & Yaffe, L. G. (1981) · Reviews of Modern Physics · doi:10.1103/revmodphys.53.43 · Cited by 2,171 · see citing works
Self-citationGasser, J., & Leutwyler, H. (1982) · Physics Reports · doi:10.1016/0370-1573(82)90035-7 · Cited by 1,753 · see citing works
Current algebra theorems for the U(1) “Goldstone boson”
Witten, E. (1979) · Nuclear Physics B · doi:10.1016/0550-3213(79)90031-2 · Cited by 1,538 · see citing works
The structure of the gauge theory vacuum
Callan, C. G., Dashen, R. F., & Gross, D. J. (1976) · Physics Letters B · doi:10.1016/0370-2693(76)90277-x · Cited by 1,264 · see citing works
Critical behavior at finite-temperature confinement transitions
Benjamin Svetitsky, B., & Yaffe, L. G. (1982) · Nuclear Physics B · doi:10.1016/0550-3213(82)90172-9 · Cited by 835 · see citing works
Toward a theory of the strong interactions
Callan, C. G., Dashen, R. F., & Gross, D. J. (1978) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.17.2717 · Cited by 752 · see citing works
Kogut, J. B., Stone, M., Wyld, H. W., Gibbs, W. R., Junko Shigemitsu, A., Shenker, S. H., & Sinclair, D. K. (1983) · Physical Review Letters · doi:10.1103/physrevlett.50.393 · Cited by 313 · see citing works
First-Order Transitions, Symmetry, and the ε Expansion
Bak, P., Krinsky, S., & Mukamel, D. (1976) · Physical Review Letters · doi:10.1103/physrevlett.36.52 · Cited by 195 · see citing works
Scales of Chiral Symmetry Breaking in Quantum Chromodynamics
Kogut, J. B., Stone, M., Wyld, H. W., Junko Shigemitsu, A., Shenker, S. H., & Sinclair, D. K. (1982) · Physical Review Letters · doi:10.1103/physrevlett.48.1140 · Cited by 194 · see citing works
Light-quark masses and isospin violation
Gross, D. J., Treiman, S. B., & Wilczek, F. A. (1979) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.19.2188 · Cited by 186 · see citing works
Self-citationDeconfining and chiral phase transitions in quantum chromodynamics at finite temperature
Banks, T., & Ukawa, A. (1983) · Nuclear Physics B · doi:10.1016/0550-3213(83)90016-0 · Cited by 149 · see citing works
Quark and Gluon Latent Heats at the Deconfinement Phase Transition in SU(3) Gauge Theory
Kogut, J. B., Matsuoka, H., Stone, M., Wyld, H. W., Shenker, S. H., Junko Shigemitsu, A., & Sinclair, D. K. (1983) · Physical Review Letters · doi:10.1103/physrevlett.51.869 · Cited by 114 · see citing works
Topological Charge in Lattice Gauge Theory
Woit, P. (1983) · Physical Review Letters · doi:10.1103/physrevlett.51.638 · Cited by 106 · see citing works
Mean field and Monte Carlo studies of SU(N) chiral models in three dimensions
Kogut, J. B., Snow, M., & Stone, M. (1982) · Nuclear Physics B · doi:10.1016/0550-3213(82)90065-7 · Cited by 87 · see citing works
Coleman-Weinberg symmetry breaking in the chiral SU(n) × SU(n) linear σ model
Paterson, A. J. (1981) · Nuclear Physics B · doi:10.1016/0550-3213(81)90489-2 · Cited by 71 · see citing works
First order transitions induced by fluctuations in general φ4-theories
Iacobson, H. H., & Amit, D. J. (1981) · Annals of Physics · doi:10.1016/0003-4916(81)90241-4 · Cited by 58 · see citing works
Radiative Decays of η and η′ as Probes of Quark Charges
Chanowitz, M. S. (1975) · Physical Review Letters · doi:10.1103/physrevlett.35.977 · Cited by 54 · see citing works
Test of Integral- and Fractional-Charged-Quark Models
Chanowitz, M. S. (1980) · Physical Review Letters · doi:10.1103/physrevlett.44.59 · Cited by 38 · see citing works
Critical behavior of linear Φ4 models with G×G′ symmetry
Pisarski, R. D., & Stein, D. L. (1981) · Physical review. B, Condensed matter · doi:10.1103/physrevb.23.3549 · Cited by 35 · see citing works
Self-citationThe renormalisation group and global G×G' theories about four dimensions
Pisarski, R. D., & Stein, D. L. (1981) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/14/12/027 · Cited by 28 · see citing works
Self-citationCalculation of the partial width for the decay η→π+π−π0
Raby, S. (1976) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.13.2594 · Cited by 11 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Witten, E. (1984) · Physical Review D · doi:10.1103/physrevd.30.272 · Cited by 3,452 · see citing works
The PHOBOS perspective on discoveries at RHIC
Back, B. B., Baker, M. D., Ballintijn, M., Barton, D. S., Becker, B., Betts, R. R., Bickley, A. A., Bindel, R., Budzanowski, A., Busza, W., et al. (2005) · Nuclear Physics A · doi:10.1016/j.nuclphysa.2005.03.084 · Cited by 2,242 · see citing works
Aoki, Y., Endrődi, G., Fodor, Z., Katz, S. D., & Szabó, K. K. (2006) · Nature · doi:10.1038/nature05120 · Cited by 1,937 · see citing works
“There are some QCD results and model calculations to determine the order of the transition at µ=0 and µ6=0 for different fermionic contents (compare refs [ 10 ; 11; 12; 13; 14; 15; 16; 17; 18; 19]).”
MethodQCD phenomenology based on a chiral effective Lagrangian
Hatsuda, T., & Kunihiro, T. (1994) · Physics Reports · doi:10.1016/0370-1573(94)90022-1 · Cited by 1,623 · see citing works
Non-perturbative renormalization flow in quantum field theory and statistical physics
Berges, J., Tetradis, N., & Wetterich, C. (2002) · Physics Reports · doi:10.1016/s0370-1573(01)00098-9 · Cited by 1,548 · see citing works
NJL-model analysis of dense quark matter
Buballa, M. (2005) · Physics Reports · doi:10.1016/j.physrep.2004.11.004 · Cited by 1,465 · see citing works
Schäfer, T., & Shuryak, E. (1998) · Reviews of Modern Physics · doi:10.1103/revmodphys.70.323 · Cited by 1,367 · see citing works
Chiral and deconfinement aspects of the QCD transition
Bazavov, A., Tanmoy Bhattacharya, A., Cheng, M., DeTar, C. E., Ding, H.-T., Gottlieb, S., Gupta, R., Hegde, P., Heller, U. M., Karsch, F., et al. (2012) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.85.054503 · Cited by 1,131 · see citing works
Signatures of the Tricritical Point in QCD
Stephanov, M. A., Rajagopal, K., & Shuryak, E. (1998) · Physical Review Letters · doi:10.1103/physrevlett.81.4816 · Cited by 1,096 · see citing works
The phase diagram of dense QCD
Fukushima, K., & Hatsuda, T. (2010) · Reports on Progress in Physics · doi:10.1088/0034-4885/74/1/014001 · Cited by 963 · see citing works
“In table 2 we summarize the Ginzburg–Landau–Wilson analysis from the chiral effective theory [36].”
BackgroundMethodInfluentialChiral effective model with the Polyakov loop
Fukushima, K. (2004) · Physics Letters B · doi:10.1016/j.physletb.2004.04.027 · Cited by 914 · see citing works
Critical Phenomena and Renormalization-Group TheoryPreprint
Andrea Pelissetto, C., & Vicari, E. (2002) · Cited by 902 · see citing works
Phases of dense quarks at large
McLerran, L., & Pisarski, R. D. (2007) · Nuclear Physics A · doi:10.1016/j.nuclphysa.2007.08.013 · Cited by 739 · see citing works
Self-citationLattice determination of the critical point of QCD at finiteTand μ
Fodor, Z., & Katz, S. D. (2002) · Journal of High Energy Physics · doi:10.1088/1126-6708/2002/03/014 · Cited by 687 · see citing works
Halász, M. Á., Jackson, A. D., Shrock, R. E., Stephanov, M. A., & Verbaarschot, J. J. M. (1998) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.58.096007 · Cited by 616 · see citing works
Color superconductivity and chiral symmetry restoration at non-zero baryon density and temperature
Berges, J., & Rajagopal, K. (1999) · Nuclear Physics B · doi:10.1016/s0550-3213(98)00620-8 · Cited by 556 · see citing works
ALICE: Physics Performance Report, Volume II
Alessandro, B., Antinori, F., Belikov, J. A., Blume, C., Dainese, A., Foka, P., Giubellino, P., Hippolyte, B., Kuhn, C. C., García, G. M., et al. (2006) · Journal of Physics G Nuclear and Particle Physics · doi:10.1088/0954-3899/32/10/001 · Cited by 550 · see citing works
Phase structure of the Polyakov-quark-meson model
Schaefer, B.-J., Pawlowski, J. M., & Wambach, J. (2007) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.76.074023 · Cited by 549 · see citing works
Phase diagrams in the three-flavor Nambu–Jona-Lasinio model with the Polyakov loop
Fukushima, K. (2008) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.77.114028 · Cited by 505 · see citing works
Quark mass and flavour dependence of the QCD phase transition
Karsch, F., Laermann, E., & Peikert, A. (2001) · Nuclear Physics B · doi:10.1016/s0550-3213(01)00200-0 · Cited by 492 · see citing works
Mapping the phases of quantum chromodynamics with beam energy scan
Bzdak, A., Esumi, S., Koch, V., Liao, J., Stephanov, M., & Xu, N. (2020) · Physics Reports · doi:10.1016/j.physrep.2020.01.005 · Cited by 465 · see citing works
“Using symmetry, universality and renormalization group considerations, it can be further argued [72] that due to the SU(3)× SU(3) chiral symmetry and the U(1)A anomaly in an idealized world with three lightest quarks (u, d and s) being massless, the finite-temperature transition must be of the first order.”
BackgroundOn the existence of a phase transition for QCD with three light quarks
Brown, F. R., Butler, F. P., Chen, H., Christ, N. H., Dong, Z., Schaffer, W., Unger, L. I., & Vaccarino, A. (1990) · Physical Review Letters · doi:10.1103/physrevlett.65.2491 · Cited by 423 · see citing works
QCD Phase Transition with Chiral Quarks and Physical Quark Masses
Tanmoy Bhattacharya, A., Buchoff, M. I., Christ, N. H., Ding, H.-T., Gupta, R., Jung, C., Karsch, F., Lin, Z., Mawhinney, R. D., McGlynn, G., et al. (2014) · Physical Review Letters · doi:10.1103/physrevlett.113.082001 · Cited by 420 · see citing works
Peláez, J. R. (2016) · Physics Reports · doi:10.1016/j.physrep.2016.09.001 · Cited by 411 · see citing works
Phase diagram of QCD in a magnetic field
Andersen, J. O., Naylor, W. R., & Anders Tranberg, B. (2016) · Reviews of Modern Physics · doi:10.1103/revmodphys.88.025001 · Cited by 387 · see citing works
Possibility of Spontaneous Parity Violation in Hot QCD
Kharzeev, D. E., Pisarski, R. D., & Tytgat, M. H. G. (1998) · Physical Review Letters · doi:10.1103/physrevlett.81.512 · Cited by 373 · see citing works
Self-citationThermodynamics of strong-interaction matter from lattice QCD
Ding, H.-T., Karsch, F., & Mukherjee, S. (2015) · International Journal of Modern Physics E · doi:10.1142/s0218301315300076 · Cited by 366 · see citing works
“If this remains significant close to the transition temperature then the relevant symmetry becomes isomorphic to that of the 3-d O(4) spin model and the transition is expected to be second order belonging to that universality class.(10,69) However, if UA(1) symmetry breaking becomes negligible near the chiral transiti…”
Gravitational Waves from a Dark Phase Transition
Schwaller, P. (2015) · Physical Review Letters · doi:10.1103/physrevlett.115.181101 · Cited by 358 · see citing works
Symmetry aspects of finite-temperature confinement transitions
Benjamin Svetitsky, B. (1986) · Physics Reports · doi:10.1016/0370-1573(86)90014-1 · Cited by 340 · see citing works
Cosmology with the Laser Interferometer Space Antenna
Auclair, P., Bacon, D., Baker, T., Barreiro, T., Bartolo, N., Belgacem, E., Bellomo, N., Ben-Dayan, I., Bertacca, D., Besançon, M., et al. (2023) · Living Reviews in Relativity · doi:10.1007/s41114-023-00045-2 · Cited by 342 · see citing works
Properties of hot and dense matter from relativistic heavy ion collisions
Braun‐Munzinger, P., Koch, V., Schäfer, T., & Stachel, J. (2016) · Physics Reports · doi:10.1016/j.physrep.2015.12.003 · Cited by 327 · see citing works
“In QCD with massless u, d and infinitely massive s, c, b, t quarks the transition is second order [61].”
BackgroundUniversality, the QCD critical and tricritical point, and the quark number susceptibility
Hatta, Y., & Ikeda, T. (2003) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.67.014028 · Cited by 334 · see citing works
Slowing out of equilibrium near the QCD critical point
Berdnikov, B. A., & Rajagopal, K. (2000) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.61.105017 · Cited by 322 · see citing works
Fermion interactions and universal behavior in strongly interacting theories
Braun, J. (2012) · Journal of Physics G Nuclear and Particle Physics · doi:10.1088/0954-3899/39/3/033001 · Cited by 322 · see citing works
Chiral phase transition within effective models with constituent quarks
Scavenius, O., Ágnes Mócsy, A., Mishustin, I. N., & Rischke, D. H. (2001) · Physical Review C · doi:10.1103/physrevc.64.045202 · Cited by 320 · see citing works
THE SEARCH FOR THE QUARK-GLUON PLASMA
Harris, J. W., & Müller, B. (1996) · Annual Review of Nuclear and Particle Science · doi:10.1146/annurev.nucl.46.1.71 · Cited by 317 · see citing works
QCD at finite temperature and chemical potential from Dyson–Schwinger equations
Fischer, C. S. (2019) · Progress in Particle and Nuclear Physics · doi:10.1016/j.ppnp.2019.01.002 · Cited by 311 · see citing works
“Assuming the UA(1) symmetry remains anomalously broken across the critical temperature, two-flavour QCD is expected to exhibit a second order phase transition in the O(4) universality class of the Heisenberg antiferromagnet [26, 409].”
BackgroundInfluentialThe physics of the quark-gluon plasma
McLerran, L. (1986) · Reviews of Modern Physics · doi:10.1103/revmodphys.58.1021 · Cited by 295 · see citing works
Scale for the Phase Diagram of Quantum Chromodynamics
Sourendu Gupta, A., Luo, X., Mohanty, B., Ritter, H. G., & Xu, N. (2011) · Science · doi:10.1126/science.1204621 · Cited by 292 · see citing works
Mizher, A. J., Chernodub, M. N., & Fraga, E. S. (2010) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.82.105016 · Cited by 282 · see citing works
Susceptibilities and the phase structure of a chiral model with Polyakov loops
Sasaki, C., Friman, B. L., & Redlich, K. (2007) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.75.074013 · Cited by 279 · see citing works
Dynamics of hot bulk QCD matter: From the quark-gluon plasma to hadronic freeze-out
Bass, S. A., & Dumitru, A. (2000) · Physical Review C · doi:10.1103/physrevc.61.064909 · Cited by 275 · see citing works
The quark-gluon plasma in equilibriumPreprint
Rischke, D. H. (2004) · Cited by 274 · see citing works
Signatures of quark-gluon plasma formation in high energy heavy-ion collisions: a critical review
Bass, S. A., Gyulassy, M., Stöcker, H., & Greiner, W. (1999) · Journal of Physics G: Nuclear and Particle Physics · doi:10.1088/0954-3899/25/3/013 · Cited by 269 · see citing works
The phase diagram of nuclear and quark matter at high baryon density
Fukushima, K., & Sasaki, C. (2013) · Progress in Particle and Nuclear Physics · doi:10.1016/j.ppnp.2013.05.003 · Cited by 259 · see citing works
QCD PHASE DIAGRAM AND THE CRITICAL POINT
Stephanov, M. A. (2005) · International Journal of Modern Physics A · doi:10.1142/s0217751x05027965 · Cited by 252 · see citing works
The chiral critical line ofNf= 2+1 QCD at zero and non-zero baryon density
de Forcrand, P., & Philipsen, O. (2007) · Journal of High Energy Physics · doi:10.1088/1126-6708/2007/01/077 · Cited by 245 · see citing works
“If the chiral limit of the Nf = 2 theory exhibits O(4) universality, then the critical line hits the axis mu,d = 0 in a tricritical point at some finite strange quark mass value m s [2].”
BackgroundThe phase diagram of the quark–meson model
Schaefer, B.-J., & Wambach, J. (2005) · Nuclear Physics A · doi:10.1016/j.nuclphysa.2005.04.012 · Cited by 240 · see citing works
QCD thermodynamics with three flavors of improved staggered quarks
Bernard, C., Burch, T., DeTar, C., Osborn, J., Gottlieb, S., Gregory, E. B., Toussaint, D., Heller, U. M., & Sugar, R. (2005) · Physical Review D · doi:10.1103/physrevd.71.034504 · Cited by 236 · see citing works
Kompaniets, M. V., & Panzer, E. (2017) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.96.036016 · Cited by 236 · see citing works
“n = 0 (self-avoiding walks): polymers [58], n = 1 (Ising universality class): liquid-vapour transitions, uniaxial magnets, n = 2 (XY universality class): superfluid λ-transition of helium [107], n = 3 (Heisenberg universality class): isotropic ferromagnets, n = 4: finite temperature QCD with two light flavours [133].”
BackgroundFuller, G. M., Mathews, G. J., & Alcock, C. R. (1988) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.37.1380 · Cited by 235 · see citing works
Kaczmarek, O., Karsch, F., Laermann, E., Miao, C., Mukherjee, S., Petreczky, P., Schmidt, C., Soeldner, W., & Unger, W. (2011) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.83.014504 · Cited by 234 · see citing works
Adams, A. W., Carr, L. D., Schäfer, T., Steinberg, P. A., & Thomas, J. E. (2012) · New Journal of Physics · doi:10.1088/1367-2630/14/11/115009 · Cited by 225 · see citing works
“In QCD with massless u,d and infinitely massive s,c,b,t quarks the transition is second order [202].”
Backgroundθ dependence of SU(N) gauge theories in the presence of a topological term
Vicari, E., & Panagopoulos, H. (2008) · Physics Reports · doi:10.1016/j.physrep.2008.10.001 · Cited by 230 · see citing works
Chiral Phase Transition Temperature in ( 2 + 1 )-Flavor QCD
Ding, H.-T., Hegde, P., Kaczmarek, O., Karsch, F., Lahiri, A., Li, S.-T., Mukherjee, S., Ohno, H., Petreczky, P., Schmidt, C., et al. (2019) · Physical Review Letters · doi:10.1103/physrevlett.123.062002 · Cited by 229 · see citing works
Susceptibilities, the specific heat, and a cumulant in two-flavor QCD
Karsch, F., & Laermann, E. (1994) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.50.6954 · Cited by 217 · see citing works
L<scp>ATTICE</scp> QCD <scp>AT</scp> F<scp>INITE</scp> T<scp>EMPERATURE</scp>
Laermann, E., & Philipsen, O. (2003) · Annual Review of Nuclear and Particle Science · doi:10.1146/annurev.nucl.53.041002.110609 · Cited by 240 · see citing works
50 Years of quantum chromodynamics
Gross, F., Klempt, E., Brodsky, S. J., A, A. J. B., Burkert, V., Heinrich, G., Jakobs, K., Meyer, C. A., Orginos, K., Strickland, M. T., et al. (2023) · The European Physical Journal C · doi:10.1140/epjc/s10052-023-11949-2 · Cited by 232 · see citing works
The QCD equation of state from the lattice
Philipsen, O. (2012) · Progress in Particle and Nuclear Physics · doi:10.1016/j.ppnp.2012.09.003 · Cited by 205 · see citing works
Susceptibilities near the QCD (tri)critical point
Schaefer, B.-J., & Wambach, J. (2007) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.75.085015 · Cited by 199 · see citing works
Thermodynamics of ( 2 + 1 )-flavor QCD: Confronting models with lattice studies
Schaefer, B.-J., Wagner, M., & Wambach, J. (2010) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.81.074013 · Cited by 194 · see citing works
Chiral transition in a strong magnetic background
Fraga, E. S., & Mizher, A. J. (2008) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.78.025016 · Cited by 190 · see citing works
New Critical Point Induced By the Axial Anomaly in Dense QCD
Hatsuda, T., Tachibana, M., Yamamoto, N., & Baym, G. (2006) · Physical Review Letters · doi:10.1103/physrevlett.97.122001 · Cited by 190 · see citing works
Hadronic spectrum of the quark plasma
DeTar, C. E., & Kogut, J. B. (1987) · Physical Review Letters · doi:10.1103/physrevlett.59.399 · Cited by 188 · see citing works
Chiral symmetry restoration at nonzero temperature in the SU(3)r×SU(3)l linear sigma model
Lenaghan, J., Rischke, D. H., & Schaffner–Bielich, J. (2000) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.62.085008 · Cited by 185 · see citing works
2+1 flavor Polyakov–Nambu–Jona-Lasinio model at finite temperature and nonzero chemical potential
Fu, W., Zhang, Z., & Liu, Y. (2008) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.77.014006 · Cited by 177 · see citing works
Critical points in the linear σ model with quarks
Bowman, E. S., & Kapusta, J. I. (2009) · Physical Review C · doi:10.1103/physrevc.79.015202 · Cited by 176 · see citing works
Measuring the hadronic spectrum of the quark plasma
DeTar, C. E., & Kogut, J. B. (1987) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.36.2828 · Cited by 173 · see citing works
Lattice QCD at non-zero temperature
Petreczky, P. (2012) · Journal of Physics G Nuclear and Particle Physics · doi:10.1088/0954-3899/39/9/093002 · Cited by 171 · see citing works
Magnetic equation of state in ( 2 + 1 )-flavor QCD
Shinji Ejiri, A., Karsch, F., Laermann, E., Miao, C., Mukherjee, S., Petreczky, P., Schmidt, C., Soeldner, W., & Unger, W. (2009) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.80.094505 · Cited by 170 · see citing works
1 THE SEARCH FOR THE QUARK- GLUON PLASMAPreprint
Harris, J. W., & Müller, B. (1996) · Cited by 170 · see citing works
Effective action for the chiral quark-meson model
Jungnickel, D.-U., & WETTERICH, C. (1996) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.53.5142 · Cited by 169 · see citing works
Character changes of pion and σ-meson at finite temperatures
Hatsuda, T., & Kunihiro, T. (1987) · Physics Letters B · doi:10.1016/0370-2693(87)91004-5 · Cited by 169 · see citing works
Vacuum fluctuations and the thermodynamics of chiral models
Skokov, V. V., Friman, B. L., Nakano, E., Redlich, K., & Schaefer, B.-J. (2010) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.82.034029 · Cited by 168 · see citing works
Optimized perturbation theory at finite temperature
Chiku, S., & Hatsuda, T. (1998) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.58.076001 · Cited by 167 · see citing works
Three-flavor chiral phase structure in hot and dense QCD matter
Schaefer, B.-J., & Wagner, M. (2009) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.79.014018 · Cited by 165 · see citing works
Hybrid Stochastic Differential Equations Applied to Quantum Chromodynamics
Duane, S., & Kogut, J. B. (1985) · Physical Review Letters · doi:10.1103/physrevlett.55.2774 · Cited by 163 · see citing works
Phase transitions in quantum chromodynamics
Meyer-Ortmanns, H. (1996) · Reviews of Modern Physics · doi:10.1103/revmodphys.68.473 · Cited by 161 · see citing works
“The most general renormalizable Lagrangian in terms of φ which is consistent with the chiral symmetry properties of QCD is given as (Pisarski and Wilczek, 1984) L = 1 2 Tr (∂µφ +)(∂µφ) − m2 2 Tr (φ+φ) − π 2 3 f1(Tr φ +φ)2 −π 2 3 f2Tr (φ +φ)2 + g · (detφ+ detφ+) .”
InfluentialAli Khan, A., Aoki, S., Burkhalter, R., Ejiri, S., Fukugita, M., Hashimoto, S., Ishizuka, N., Iwasaki, Y., Kanaya, K., Kaneko, T., et al. (2000) · Physical Review D · doi:10.1103/physrevd.63.034502 · Cited by 158 · see citing works
Fischer, T., Sagert, I., Pagliara, G., Hempel, M., Schaffner-Bielich, J., Rauscher, T., Thielemann, F.-K., Käppeli, R., Martínez-Pinedo, G., & Liebendörfer, M. (2011) · The Astrophysical Journal Supplement Series · doi:10.1088/0067-0049/194/2/39 · Cited by 158 · see citing works
“On the other hand, field theoretical and phenomenological calculations point to a first order phase transition from hadronic to quark matter at large chemical potentials and finite temperatures (see Berges & Rajagopal 1999; Klevansky 1992; Pisarski & Wilczek 1984).”
BackgroundChiral phase boundary of QCD at finite temperature
Braun, J., & Holger Gies, A. (2006) · Journal of High Energy Physics · doi:10.1088/1126-6708/2006/06/024 · Cited by 158 · see citing works
Snellings, R. J. M. (2011) · New Journal of Physics · doi:10.1088/1367-2630/13/5/055008 · Cited by 154 · see citing works
Accidental composite dark matter
Antipin, O., Michele Redi, B., Струмиа, А., & Vigiani, E. (2015) · Journal of High Energy Physics · doi:10.1007/jhep07(2015)039 · Cited by 153 · see citing works
“For SU(N) with NTF massless flavours this is believed to happen in the window 3 ≤ NTF ≤ 4N and N > 3 [45].”
BackgroundFinite size effects on measures of critical exponents in d = 3 O(N) models
Ballesteros, H. G., Fernández, L. A., Martín-Mayor, V., & Sudupe, A. M. (1996) · Physics Letters B · doi:10.1016/0370-2693(96)00984-7 · Cited by 152 · see citing works
Volume fluctuations and higher-order cumulants of the net baryon number
Skokov, V. V., Friman, B. L., & Redlich, K. (2013) · Physical Review C · doi:10.1103/physrevc.88.034911 · Cited by 149 · see citing works
Heavy quarks and jets as probes of the QGP
Apolinário, L., Lee, Y.-J., & Winn, M. (2022) · Progress in Particle and Nuclear Physics · doi:10.1016/j.ppnp.2022.103990 · Cited by 148 · see citing works
Phase Transitions in the Early and Present Universe
Boyanovsky, D., de Vega, H. J., & Schwarz, D. J. (2006) · Annual Review of Nuclear and Particle Science · doi:10.1146/annurev.nucl.56.080805.140539 · Cited by 146 · see citing works
Yang Bai, A., Long, A. J., & Lu, S. Q. (2019) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.99.055047 · Cited by 147 · see citing works
“Nevertheless, a model with Nf = 1 is not expected to have a first-order phase transition [47] or allow for the formation of dQNs.”
BackgroundMethodInfluentialQCD-Electroweak First-Order Phase Transition in a Supercooled Universe
Iso, S., Serpico, P. D., & Shimada, K. (2017) · Physical Review Letters · doi:10.1103/physrevlett.119.141301 · Cited by 146 · see citing works
“The chiral symmetry is thus broken from SU(6)L × SU(6)R to SU(6), and the associated PT is then first-order [18].”
BackgroundThe Chiral Critical Point in 3-Flavour QCDPreprint
Schmidta, C., Karscha, F., & Laermanna, E. (2001) · Cited by 145 · see citing works
Deuzeman, A., Lombardo, M. P., & Elisabetta Pallante, A. (2008) · Physics Letters B · doi:10.1016/j.physletb.2008.10.039 · Cited by 144 · see citing works
Quarkyonic matter and chiral symmetry breaking
McLerran, L., Redlich, K., & Sasaki, C. (2009) · Nuclear Physics A · doi:10.1016/j.nuclphysa.2009.04.001 · Cited by 144 · see citing works
Relevance of the axial anomaly at the finite-temperature chiral transition in QCD
Andrea Pelissetto, C., & Vicari, E. (2013) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.88.105018 · Cited by 138 · see citing works
Polyakov loop modeling for hot QCD
Fukushima, K., & Skokov, V. V. (2017) · Progress in Particle and Nuclear Physics · doi:10.1016/j.ppnp.2017.05.002 · Cited by 138 · see citing works
“(130), and the order of the phase transition must be first [110].”
BackgroundThermalization of fermionic quantum fields
Berges, J., Borsányi, S., & Serreau, J. (2003) · Nuclear Physics B · doi:10.1016/s0550-3213(03)00261-x · Cited by 137 · see citing works
QCD critical region and higher moments for three-flavor models
Schaefer, B.-J., & Wagner, M. (2012) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.85.034027 · Cited by 137 · see citing works
The chiral critical point in 3-flavour QCD
Karsch, F., Laermann, E., & Schmidt, C. (2001) · Physics Letters B · doi:10.1016/s0370-2693(01)01114-5 · Cited by 136 · see citing works
Amplification of cosmological inhomogeneities by the QCD transition
Schmid, C., Schwarz, D. J., & Widerin, P. (1999) · Physical Review D · doi:10.1103/physrevd.59.043517 · Cited by 132 · see citing works
Critical exponents of new universality classes
Rosenstein, B., Yu, H.-L., & Kovner, A. (1993) · Physics Letters B · doi:10.1016/0370-2693(93)91253-j · Cited by 132 · see citing works
Phase structure and thermodynamics of QCD
Herbst, T. K., Pawlowski, J. M., & Schaefer, B.-J. (2013) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.88.014007 · Cited by 131 · see citing works
- Authors
- Pisarski, R. D., & Wilczek, F.
- Affiliations
- University of California, Santa Barbara (US)
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 1984-01-15
- Volume
- 29
- Issue
- 2
- Pages
- 338-341
- ISSN
- 0556-2821 (ISSN-L)
- OpenAlex
- W2107120226
- Cited by
- 1,252
- References
- 23
- Citations by year
- 2026: 33 · 2025: 41 · 2024: 51 · 2023: 57 · 2022: 69 · 2021: 54 · 2020: 47 · 2019: 57 · 2018: 28 · 2017: 40 · 2016: 42 · 2015: 36 · 2014: 34 · 2013: 40 · 2012: 43
- FWCI
- 9.58
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
- Topics
- 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 › High-Energy Particle Collisions Research
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Particle physics theoretical and experimental studies
- Keywords
- chiral phase transition, chiral symmetry restoration, linear sigma model, epsilon expansion, first-order phase transition, finite temperature, massless fermions, QCD
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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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