Phase transitions in quantum chromodynamics
Open accessAbstract
The current understanding of finite-temperature phase transitions in QCD is reviewed. A critical discussion of refined phase-transition criteria in numerical lattice simulations and of analytical tools going beyond the mean-field level in effective continuum models for QCD is presented. Theoretical predictions about the order of the transitions are compared with possible experimental manifestations in heavy-ion collisions. Various places in phenomenological descriptions are pointed out where more reliable data for QCD's equation of state would help in selecting the most realistic scenario among those proposed. Unanswered questions are raised about the relevance of calculations that assume thermodynamic equilibrium. Promising new approaches for implementing nonequilibrium aspects of the thermodynamics of heavy-ion collisions are described. [S0034-6861(96)00302-9]
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When the screening length of the color force is smaller than the size of the cc bound state, this narrow resonance will melt.
“The original suggestion [130] is that when the screening length of the color force is smaller than the size of the ¯ cc bound state, this narrow resonance will melt.”
From Phase Transitions in the Early and Present Universe (2006) · cites this paper as [130]
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“In the Langevin algorithm (Parisi and Wu, 1981; Fukugita and Ukawa, 1985; Batrouni et al., 1985) the equation of motion is a partial differential equation, which is of first order in time.”
Hadronic interactions of high energy cosmic-ray observed by emulsion chambers
Lattes, C. M. G., Fujimoto, Y., & Hasegawa, S. (1980) · Physics Reports · doi:10.1016/0370-1573(80)90165-9 · Cited by 370 · see citing works
Chemical potential on the lattice
Hasenfratz, P., & Karsch, F. (1983) · Physics Letters B · doi:10.1016/0370-2693(83)91290-x · Cited by 362 · see citing works
Deducing hard thermal loops from Ward identities
Braaten, E., & Pisarski, R. D. (1990) · Nuclear Physics B · doi:10.1016/0550-3213(90)90351-d · Cited by 360 · cited 1× · see citing works
“At extremely high temperatures, T ≫ ΛMS , with typical momenta Q ≈ T , the coupling Q2/Λ2MS becomes weak, and resummed finite temperature perturbation theory (Braaten and Pisarski, 1990 and 1992) may be applied.”
Pion interferometry of quark-gluon plasma
Pratt, S. (1986) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.33.1314 · Cited by 354 · see citing works
Pion Interferometry for Exploding Sources
Pratt, S. (1984) · Physical Review Letters · doi:10.1103/physrevlett.53.1219 · Cited by 342 · 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
First-Order Phase Transitions in Renormalization-Group Theory
Nienhuis, B., & Nauenberg, M. (1975) · Physical Review Letters · doi:10.1103/physrevlett.35.477 · Cited by 328 · cited 1× · see citing works
“First order transitions are then associated with a discontinuity fixed point at zero temperature (Nienhuis and Nauenberg, 1975; van Leeuwen, 1975).”
Hove, L. V. (1982) · Physics Letters B · doi:10.1016/0370-2693(82)90617-7 · Cited by 326 · see citing works
Theory and phenomenology of the QCD vacuum
Shuryak, E. (1984) · Physics Reports · doi:10.1016/0370-1573(84)90037-1 · Cited by 320 · see citing works
Multiplicities,p T distributions and the expected hadron → quark-gluon phase transition
Hagedorn, R. (1983) · Rivista Del Nuovo Cimento · doi:10.1007/bf02740917 · Cited by 318 · see citing works
Finite-size scaling and Monte Carlo simulations of first-order phase transitions
Lee, J., & Kosterlitz, J. M. (1991) · Physical review. B, Condensed matter · doi:10.1103/physrevb.43.3265 · Cited by 316 · see citing works
A rigorous theory of finite-size scaling at first-order phase transitions
Borgs, C., & Kotecký, R. (1990) · Journal of Statistical Physics · doi:10.1007/bf01013955 · Cited by 316 · cited 2× · see citing works
“(The approach of Borgs and Kotecky (1990) comes closest to a rigorous derivation.)”
Possible evidence for Abelian dominance in quark confinement
Suzuki, T., & Yotsuyanagi, I. (1990) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.42.4257 · Cited by 311 · see citing works
Monte Carlo computations in lattice gauge theories
Creutz, M. J., Jacobs, L. A., & Claudio Rebbi, B. (1983) · Physics Reports · doi:10.1016/0370-1573(83)90016-9 · Cited by 309 · cited 2× · see citing works
“For pedagogical introductions we refer to the literature (see e.g. (Kogut, 1983; Creutz et al., 1983) or more recently (Rothe, 1992; Montvay and Münster, 1994)).”
Condensation of a Classical Gas with Long-Range Attraction
van Kampen, N. G. (1964) · Physical Review · doi:10.1103/physrev.135.a362 · Cited by 308 · see citing works
The 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
Transport coefficients of QCD matter
Hosoya, A., & Kajantie, K. (1985) · Nuclear Physics B · doi:10.1016/0550-3213(85)90499-7 · Cited by 291 · see citing works
Transverse interactions and transport in relativistic quark-gluon and electromagnetic plasmas
Baym, G., Monien, H., Pethick, C. J., & Ravenhall, D. G. (1990) · Physical Review Letters · doi:10.1103/physrevlett.64.1867 · Cited by 290 · see citing works
Resummation and gauge invariance of the gluon damping rate in hot QCD
Braaten, E., & Pisarski, R. D. (1990) · Physical Review Letters · doi:10.1103/physrevlett.64.1338 · Cited by 289 · cited 1× · see citing works
“At extremely high temperatures, T ≫ ΛMS , with typical momenta Q ≈ T , the coupling Q2/Λ2MS becomes weak, and resummed finite temperature perturbation theory (Braaten and Pisarski, 1990 and 1992) may be applied.”
Two-scale-factor universality and the renormalization group
Hohenberg, P. C., Amnon Aharony, A., Halperin, B. I., & Siggia, E. D. (1976) · Physical review. B, Solid state · doi:10.1103/physrevb.13.2986 · Cited by 278 · see citing works
Feynman-Graph Expansion for the Equation of State near the Critical Point
Brézin, E., Wallace, D. J., & Wilson, K. G. (1973) · Physical review. B, Solid state · doi:10.1103/physrevb.7.232 · Cited by 275 · see citing works
Blöte, H. W. J., & Nightingale, M. P. (1982) · Physica A Statistical Mechanics and its Applications · doi:10.1016/0378-4371(82)90187-x · Cited by 274 · cited 1× · see citing works
“(3.32) The ‘critical’ correlation length ξ (p) L (βc, L) diverges at βc in the infinite volume limit also in the case of a first order transition (Blöte and Nightingale, 1982; Privman and Fisher, 1983).”
InfluentialThe qualitative behavior of Yang-Mills theory in 2 + 1 dimensions
Feynman, R. P. (1981) · Nuclear Physics B · doi:10.1016/0550-3213(81)90005-5 · Cited by 268 · cited 1× · see citing works
“Three dimensional SU(N) gauge theories show an area-law for Wilson loops (Feynman, 1981) with short range correlations.”
Relativistic quantum molecular dynamics approach to nuclear collisions at ultrarelativistic energies
Sorge, H., STÖCKER, H., & Greiner, W. (1989) · Nuclear Physics A · doi:10.1016/0375-9474(89)90641-6 · Cited by 268 · see citing works
SU(N) gauge theory couplings on asymmetric lattices
Karsch, F. (1982) · Nuclear Physics B · doi:10.1016/0550-3213(82)90390-x · Cited by 265 · cited 2× · see citing works
“(3.20) The coefficients cσ and cτ have been perturbatively determined by Karsch (1982).”
InfluentialEmergence of coherent long wavelength oscillations after a quench: application to QCD
Rajagopal, K., & Wilczek, F. A. (1993) · Nuclear Physics B · doi:10.1016/0550-3213(93)90591-c · Cited by 264 · cited 3× · see citing works
“Methods of nonequilibrium physics and the powerful concept of dynamical universality classes become applicable, if the hot plasma is quenched via almost instantaneous cooling (Rajagopal and Wilczek, 1993).”
Linear sigma model with parity doubling
DeTar, C. E., & Kunihiro, T. (1989) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.39.2805 · Cited by 261 · see citing works
Two-stage equilibration in high energy heavy ion collisions
Shuryak, E. (1992) · Physical Review Letters · doi:10.1103/physrevlett.68.3270 · Cited by 253 · see citing works
Gyulassy, M., Kajantie, K., Kurki-Suonio, H., & McLerran, L. (1984) · Nuclear Physics B · doi:10.1016/0550-3213(84)90004-x · Cited by 251 · see citing works
Hydrodynamic Model of the Condensation of a Vapor near Its Critical Point
Langer, J. S., & Turski, Ł. A. (1973) · Physical Review A · doi:10.1103/physreva.8.3230 · Cited by 251 · see citing works
Cosmological baryon diffusion and nucleosynthesis
Applegate, J. H., Hogan, C. J., & Scherrer, R. J. (1987) · Physical Review D · doi:10.1103/physrevd.35.1151 · Cited by 246 · cited 1× · see citing works
“…inhomogeneities had survived until the epoch of primordial nucleosynthesis, they may have influenced the light element abundances and led to deviations from values obtained in the standard scenario (without a phase transition) (Schramm et al., 1992; Fuller et al., 1988; Applegate et al., 1987).”
Nonequilibrium thermodynamics in field theory: Transport coefficients
Hosoya, A., Sakagami, M., & Takao, M. (1984) · Annals of Physics · doi:10.1016/0003-4916(84)90144-1 · Cited by 243 · see citing works
Pion interferometry in ultrarelativistic heavy-ion collisions
Bertsch, G. F., Gong, M., & Tohyama, M. (1988) · Physical Review C · doi:10.1103/physrevc.37.1896 · Cited by 243 · see citing works
Hydrodynamics of ultra-relativistic heavy ion collisions
Baym, G., Friman, B. L., Blaizot, J.-P., Soyeur, M., & Czyz, W. (1983) · Nuclear Physics A · doi:10.1016/0375-9474(83)90666-8 · Cited by 243 · see citing works
Calculation of the gluon damping rate in hot QCD
Braaten, E., & Pisarski, R. D. (1990) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.42.2156 · Cited by 240 · cited 1× · see citing works
“At extremely high temperatures, T ≫ ΛMS , with typical momenta Q ≈ T , the coupling Q2/Λ2MS becomes weak, and resummed finite temperature perturbation theory (Braaten and Pisarski, 1990 and 1992) may be applied.”
Strange anti-baryons from quark-gluon plasma
Johann Rafelski, A. (1991) · Physics Letters B · doi:10.1016/0370-2693(91)91576-h · Cited by 240 · see citing works
Fuller, 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 · cited 1× · see citing works
“…inhomogeneities had survived until the epoch of primordial nucleosynthesis, they may have influenced the light element abundances and led to deviations from values obtained in the standard scenario (without a phase transition) (Schramm et al., 1992; Fuller et al., 1988; Applegate et al., 1987).”
First-order phase transition in the SU(3) gauge theory at finite temperature
Yaffe, L. G., & Svetitsky, B. (1982) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.26.963 · Cited by 228 · see citing works
Meson properties at finite temperature and baryon density
Lutz, M. F. M., Klimt, S., & Weise, W. (1992) · Nuclear Physics A · doi:10.1016/0375-9474(92)90256-j · Cited by 224 · see citing works
Effective Lagrangian with two color-singlet gluon fields
Schechter, J. (1980) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.21.3393 · Cited by 223 · see citing works
Thermal equilibration in ultra-relativistic heavy-ion collisions
Baym, G. (1984) · Physics Letters B · doi:10.1016/0370-2693(84)91863-x · Cited by 221 · see citing works
Monte Carlo integration for lattice gauge theories with fermions
Weingarten, D., & Petcher, D. N. (1981) · Physics Letters B · doi:10.1016/0370-2693(81)90112-x · Cited by 220 · see citing works
APPLICATION OF THE RENORMALIZATION GROUP TO A SECOND-ORDER QCD PHASE TRANSITION
Wilczek, F. A. (1992) · International Journal of Modern Physics A · doi:10.1142/s0217751x92001757 · Cited by 219 · cited 2× · see citing works
“These may also lead to observable consequences (Bialas and Peschanski, 1988; Wilczek, 1992; Rajagopal and Wilczek, 1993; Bjorken et al., 1993; Gavin et al., 1994a and b), in analogy to the well-known phenomenon of critical opalescence.”
Generalized beth-uhlenbeck approach for hot nuclear matter
Schmidt, M., RÖPKE, G., & Schulz, H. (1990) · Annals of Physics · doi:10.1016/0003-4916(90)90340-t · Cited by 218 · 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
The QCD Vacuum, Hadrons and Superdense Matter
Shuryak, E. (1988) · World Scientific lecture notes in physics · doi:10.1142/0161 · Cited by 209 · see citing works
Equation of State for the SU(3) Gauge Theory
Boyd, G., Engels, J., Karsch, F., Laermann, E., Legeland, C., Lütgemeier, M., & Petersson, B. (1995) · Physical Review Letters · doi:10.1103/physrevlett.75.4169 · Cited by 205 · cited 1× · see citing works
“The Nτ -dependence has been studied in case of the SU(3)-deconfinement transition by Boyd et al. (1995) (see also Karsch and Laermann, 1995).”
Dilepton radiation from high temperature nuclear matter
Gale, C., & Kapusta, J. I. (1987) · Physical Review C · doi:10.1103/physrevc.35.2107 · Cited by 204 · see citing works
Diagnosing quark matter by measuring the total entropy and the photon or dilepton emission rates
Hwa, R. C., & Kajantie, K. (1985) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.32.1109 · Cited by 201 · 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 · cited 2× · see citing works
“Examples are known (Bak et al., 1976), where the results to leading order in ε remain a good guide for ε = 1.”
The hydrodynamics of hadron matter under a pion interferometric microscope
Makhlin, A., & Sinyukov, Y. M. (1988) · The European Physical Journal C · doi:10.1007/bf01560393 · Cited by 192 · see citing works
Nambu-Jona-Lasinio-like models and the low-energy effective action of QCD
Bijnens, J., Bruno, C., & de Rafael, E. (1993) · Nuclear Physics B · doi:10.1016/0550-3213(93)90466-3 · Cited by 191 · see citing works
Microcanonical Ensemble Formulation of Lattice Gauge Theory
Callaway, D. J. E., & Rahman, A. (1982) · Physical Review Letters · doi:10.1103/physrevlett.49.613 · Cited by 190 · cited 1× · see citing works
“The microcanonical algorithm (Callaway and Rahman, 1982 and 1983) is based on the observation that the Euclidean path integral of a quantum field theory in four dimensions can be written as a partition function for a system of classical statistical mechanics in 4 spatial dimensions with a canonical…”
Finite-size rounding of a first-order phase transition
Imry, Y. (1980) · Physical review. B, Condensed matter · doi:10.1103/physrevb.21.2042 · Cited by 190 · cited 1× · see citing works
“A phenomenological approach has been developed by (Imry, 1980; Fisher and Berker, 1982; Privman and Fisher, 1983; Binder and Landau, 1984; Challa et al., 1986).”
Non-perturbative thermodynamics of SU (N) gauge theories
Engels, J., Fingberg, J., Karsch, F., Miller, D. E., & Weber, M. (1990) · Physics Letters B · doi:10.1016/0370-2693(90)90496-s · Cited by 189 · cited 3× · see citing works
“In this section we summarize the lattice expressions of thermodynamic quantities and outline an approach due to Engels et al. (1990b) to derive the equation of state in an entirely nonperturbative framework.”
Nature of the Deconfining Phase Transition in SU(3) Lattice Gauge Theory
Brown, F. R., Christ, N. H., Deng, Y., Gao, M., & Woch, T. J. (1988) · Physical Review Letters · doi:10.1103/physrevlett.61.2058 · Cited by 189 · cited 2× · see citing works
“Brown et al. (1988) have performed a concurrent study to Bacilieri et al. (1988).”
Limitations to dimensional reduction at high temperature
Landsman, N. P. (1989) · Nuclear Physics B · doi:10.1016/0550-3213(89)90424-0 · Cited by 183 · see citing works
Pion interferometry as a probe of the plasma
Bertsch, G. F. (1989) · Nuclear Physics A · doi:10.1016/0375-9474(89)90597-6 · Cited by 182 · see citing works
Kaon and pion production in central Si+Au collisions at 14.6AGeV/c
Abbott, T., Akiba, Y., Alburger, D. E., Beavis, D., Betts, R. R., Birstein, L., Bloomer, M. A., Bond, P. D., Chasman, C., Chu, Y. Y., et al. (1990) · Physical Review Letters · doi:10.1103/physrevlett.64.847 · Cited by 180 · see citing works
Nucleation of relativistic first-order phase transitions
Csernai, L. P., & Kapusta, J. I. (1992) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.46.1379 · Cited by 180 · see citing works
Glueball spectroscopy in 4d SU(3) lattice gauge theory (I)
Berg, B. A., & Billoire, A. H. (1983) · Nuclear Physics B · doi:10.1016/0550-3213(83)90620-x · Cited by 176 · see citing works
Bubble growth and droplet decay in the quark-hadron phase transition in the early Universe
Kajantie, K., & Kurki-Suonio, H. (1986) · Physical Review D · doi:10.1103/physrevd.34.1719 · Cited by 174 · see citing works
Intermittency parameters as a possible signal for quark-gluon plasma formation
Białas, A., & Hwa, R. C. (1991) · Physics Letters B · doi:10.1016/0370-2693(91)91747-j · Cited by 173 · see citing works
Stochastic quantization versus the microcanonical ensemble: Getting the best of both worlds
Duane, S. (1985) · Nuclear Physics B · doi:10.1016/0550-3213(85)90369-4 · Cited by 173 · cited 1× · see citing works
“The stochastic hybrid algorithm (Duane, 1985) interrupts the integration of Hamilton’s equation of motion along a single trajectory with fixed energy.”
Ochs, W., & Wosiek, J. (1988) · Physics Letters B · doi:10.1016/0370-2693(88)90131-1 · Cited by 169 · see citing works
Nonequilibrium evolution of scalar fields in FRW cosmologies
Boyanovsky, D., de Vega, H. J., & Holman, R. (1994) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.49.2769 · Cited by 167 · see citing works
New Monte Carlo Technique for Studying Phase Transitions
Ferrenberg, A. M., & Swendsen, R. H. (1989) · Physical Review Letters · doi:10.1103/physrevlett.63.1658.2 · Cited by 164 · see citing works
Abelian dominance in SU (2) color confinement
Hioki, S., Kitahara, S.-I., Kiura, S., Matsubara, Y., Miyamura, O., Ohno, S., & Suzuki, T. (1991) · Physics Letters B · doi:10.1016/0370-2693(91)91838-m · Cited by 162 · see citing works
Quark matter formation and heavy ion collisions
Jacob, M., & Vân, J. T. T. (1982) · Physics Reports · doi:10.1016/0370-1573(82)90083-7 · Cited by 161 · see citing works
The order of the deconfinement transition in SU(3) Yang-Mills theory
Çelik, T., Engels, J., & Satz, H. (1983) · Physics Letters B · doi:10.1016/0370-2693(83)91314-x · Cited by 158 · cited 3× · see citing works
“Celik et al. (1983) have recorded two-state signals from hot and cold starts, indicating two coexisting phases with different expectation values of the Wilson line at the critical coupling.”
Phase transition from strong-coupling expansion
Polonyi, J., & Szlachányi, K. (1982) · Physics Letters B · doi:10.1016/0370-2693(82)91280-1 · Cited by 155 · see citing works
Narison, S. (1990) · World Scientific lecture notes in physics · doi:10.1142/0647 · Cited by 153 · see citing works
Bervillier, C. (1976) · Physical review. B, Solid state · doi:10.1103/physrevb.14.4964 · Cited by 152 · see citing works
Rothe, H. J. (1992) · World Scientific lecture notes in physics · doi:10.1142/1268 · Cited by 150 · see citing works
Dynamics of the QCD phase transition
Csernai, L. P., & Kapusta, J. I. (1992) · Physical Review Letters · doi:10.1103/physrevlett.69.737 · Cited by 149 · see citing works
Deconfining 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 · cited 1× · see citing works
“The integration over quark degrees of freedom induces an external field on the effective level of spin models (Banks and Ukawa, 1983; DeGrand and DeTar, 1983).”
Monopoles and string tension in SU(2) QCD
Shiba, H., & Suzuki, T. (1994) · Physics Letters B · doi:10.1016/0370-2693(94)90168-6 · Cited by 149 · see citing works
Renormalization-group approach to domain-growth scaling
Bray, A. J. (1990) · Physical review. B, Condensed matter · doi:10.1103/physrevb.41.6724 · Cited by 149 · see citing works
Hatsuda, T., & Kunihiro, T. (1985) · Progress of Theoretical Physics · doi:10.1143/ptp.74.765 · Cited by 146 · see citing works
Chiral phase transition in the SU(3) Nambu and Jona-Lasinio model
Klimt, S., Lutz, M. F. M., & Weise, W. (1990) · Physics Letters B · doi:10.1016/0370-2693(90)91003-t · Cited by 146 · see citing works
Canonical ensembles and nonzero density quantum chromodynamics
Anna Hasenfratz, A., & Toussaint, D. (1992) · Nuclear Physics B · doi:10.1016/0550-3213(92)90247-9 · Cited by 146 · see citing works
Variant actions and phase structure in lattice gauge theory
Bhanot, G., & Creutz, M. J. (1981) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.24.3212 · Cited by 146 · see citing works
Kajantie, K., & Matsui, T. (1985) · Physics Letters B · doi:10.1016/0370-2693(85)90343-0 · Cited by 145 · see citing works
The QCD Vacuum, Hadrons and Superdense Matter
Shuryak, E. (2004) · World Scientific lecture notes in physics · doi:10.1142/5367 · Cited by 143 · cited 7× · see citing works
“An important class of models for the gluonic sector are instanton descriptions of the QCD vacuum (Shuryak, 1984). The idea is that the most important (nonperturbative) contributions to the QCD-partition function come from instantons and anti-instantons at short distance scales. Dynakonov and Mirlin (1988) and Kanki (1…”
InfluentialQuark-gluon transport theory II. Color response and color correlations in a quark-gluon plasma
Heinz, U. (1986) · Annals of Physics · doi:10.1016/0003-4916(86)90114-4 · Cited by 141 · see citing works
Finite-size scaling for Potts models
Borgs, C., Kotecký, R., & Miracle-Sol�, S. (1991) · Journal of Statistical Physics · doi:10.1007/bf01017971 · Cited by 140 · cited 1× · see citing works
“More recently exact results have been obtained by Borgs and Kotecky (1990) and Borgs et al. (1991) for models which can be represented by a contour expansion with small activities like the q-state Potts model for large q.”
Where Is the Continuum in Lattice Quantum Chromodynamics?
Kennedy, A. D., Kuti, J., Meyer, S., & Pendleton, B. J. (1985) · Physical Review Letters · doi:10.1103/physrevlett.54.87 · Cited by 137 · see citing works
Zel’dovich, Y. B., Molchanov, S. A., Ruzmaikin, A. A., & Sokoloff, D. D. (1987) · Uspekhi Fizicheskih Nauk · doi:10.3367/ufnr.0152.198705a.0003 · Cited by 134 · see citing works
The effect of small particles on fluid turbulence in a flat-plate, turbulent boundary layer in air
Rogers, C., & Eaton, J. K. (1991) · Physics of Fluids A Fluid Dynamics · doi:10.1063/1.857969 · Cited by 133 · see citing works
Rates for dilepton production at RHIC and LHC between the and υ are big
Kapusta, J. I., McLerran, L., & Srivastava, D. K. (1992) · Physics Letters B · doi:10.1016/0370-2693(92)91445-f · Cited by 132 · see citing works
Temperature measurement of quark-gluon plasma formed in high energy nucleus-nucleus collisions
Kajantie, K., & Miettinen, H. I. (1981) · The European Physical Journal C · doi:10.1007/bf01548770 · Cited by 130 · see citing works
Langevin Simulation Including Dynamical Quark Loops
Ukawa, A., & Fukugita, M. (1985) · Physical Review Letters · doi:10.1103/physrevlett.55.1854 · Cited by 128 · see citing works
Transverse-momentum dependence of J/Ψ production in nuclear collisions
Gavin, S., & Gyulassy, M. (1988) · Physics Letters B · doi:10.1016/0370-2693(88)91476-1 · Cited by 126 · see citing works
How to make large domains of disoriented chiral condensate
Gavin, S., Gocksch, A., & Pisarski, R. D. (1994) · Physical Review Letters · doi:10.1103/physrevlett.72.2143 · Cited by 126 · cited 1× · see citing works
“These may also lead to observable consequences (Bialas and Peschanski, 1988; Wilczek, 1992; Rajagopal and Wilczek, 1993; Bjorken et al., 1993; Gavin et al., 1994a and b), in analogy to the well-known phenomenon of critical opalescence.”
Electromagnetic probes of quark-gluon plasma in relativistic heavy-ion collisions
Ruuskanen, P. V. (1992) · Nuclear Physics A · doi:10.1016/0375-9474(92)90572-2 · Cited by 125 · see citing works
Intermittency and critical behaviour
Satz, H. (1989) · Nuclear Physics B · doi:10.1016/0550-3213(89)90546-4 · Cited by 123 · see citing works
Calculation of the quark damping rate in hot QCD
Braaten, E., & Pisarski, R. D. (1992) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.46.1829 · Cited by 123 · see citing works
Strong coupling QCD at finite baryon-number density
Karsch, F., & Mütter, K.-H. (1989) · Nuclear Physics B · doi:10.1016/0550-3213(89)90396-9 · Cited by 122 · see citing works
Order of the deconfining phase transition in SU(3) lattice gauge theory
Fukugita, M., Okawa, M., & Ukawa, A. (1989) · Physical Review Letters · doi:10.1103/physrevlett.63.1768 · Cited by 121 · cited 5× · see citing works
“The deconfinement transition is now believed to be of first order for three colors (Fukugita et al., 1989; Gavai et al., 1989), and the equation of state is known in the limit of infinite quark masses (Engels et al., 1990b; Laermann et al., 1995).”
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“c of a first-order transition. As an additional cross-check we have made another three-parameter fit to the generic functional form of a large-N4 expansion of κc 0(N4), valid at a first-order transition [33], namely, κc 0(N4) = κ c 0(∞)− C/N4 − D/N2 4 +O(1/N3 4). (8) 13 -2.00e-04 -1.95e-04 -1.90e-04 -1.85e-04 -1.80e-04 -…”
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Dynamical viscosity of nucleating bubbles
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Quantum Spin Ice in Three-Dimensional Rydberg Atom Arrays
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Exploring axial U(1) restoration in a modified 2+1 flavor Polyakov–quark–meson model
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Relaxing near the critical point
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MULTIFRAGMENTATIONS OF TARGETS AT SPS ENERGY — EVIDENCE OF BOTH MONOFRACTALITY AND MULTIFRACTALITY
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Antoniou, N. G., Diakonos, F. Κ., & Kapoyannis, A. S. (2010) · Physical Review C · doi:10.1103/physrevc.81.011901 · Cited by 11 · see citing works
Phase transitions in the early and the present Universe: from the big bang to heavy ion collisions
Boyanovsky, D. (2001) · Springer eBooks · doi:10.1007/978-94-010-0997-3_1 · Cited by 11 · see citing works
A Brief Review of Chiral Chemical Potential and Its Physical Effects
Yang, L.-K., Luo, X., Segovia, J., & Zong, H.-S. (2020) · Symmetry · doi:10.3390/sym12122095 · Cited by 10 · see citing works
“As the temperature increases, the strong interaction matter will undergo a deconfinement phase transition from hadronic matter to quark–gluon plasma [44,45].”
BackgroundTHERMAL RENORMALONS IN SCALAR FIELD THEORY
Loewe, M., & Valenzuela, C. (2000) · Modern Physics Letters A · doi:10.1142/s0217732300001481 · Cited by 10 · see citing works
A heavy quark–antiquark pair in hot QCD
Антонов, Д. В., Domdey, S., & Pirner, H. J. (2007) · Nuclear Physics A · doi:10.1016/j.nuclphysa.2007.03.009 · Cited by 10 · see citing works
Rai, S. K., & Tiwari, V. K. (2022) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.105.094010 · Cited by 9 · see citing works
Murgana, F., Koenigstein, A., & Rischke, D. H. (2023) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.108.116016 · Cited by 9 · see citing works
Phase structure of the on-shell parametrized 2 + 1 flavor Polyakov quark-meson model
Rai, S. K., & Tiwari, V. K. (2024) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.109.034025 · Cited by 9 · see citing works
- Authors
- Meyer-Ortmanns, H.
- Venue
- Reviews of Modern Physics
- Publisher
- American Physical Society (APS)
- Published
- 1996-04-01
- Volume
- 68
- Issue
- 2
- Pages
- 473-598
- ISSN
- 0034-6861 (ISSN-L)
- 1539-0756
- OpenAlex
- W1971177656
- Cited by
- 161
- References
- 450
- Citations by year
- 2026: 1 · 2025: 5 · 2024: 4 · 2023: 4 · 2022: 5 · 2021: 3 · 2020: 6 · 2019: 4 · 2018: 2 · 2017: 1 · 2015: 7 · 2014: 5 · 2013: 5 · 2012: 6
- FWCI
- 6.22
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Reviews of Modern Physics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- 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
- QCD, finite-temperature phase transition, QCD phase diagram, critical phenomena, lattice QCD, mean-field theory, order of phase transition, heavy-ion collisions, QCD equation of state, non-equilibrium thermodynamics, thermodynamic equilibrium
About these checks
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.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
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