42:
2323:
2929:
2829:
1237:), while the gluon fields are defined on the links connecting neighboring sites. This approximation approaches continuum QCD as the spacing between lattice sites is reduced to zero. Because the computational cost of numerical simulations can increase dramatically as the lattice spacing decreases, results are often
1399:
The lattice discretization means approximating continuous and infinite space-time by a finite lattice spacing and size. The smaller the lattice, and the bigger the gap between nodes, the bigger the error. Limited resources commonly force the use of smaller physical lattices and larger lattice spacing
1990:
Bennett, Ed; Lucini, Biagio; Del Debbio, Luigi; Jordan, Kirk; Patella, Agostino; Pica, Claudio; Rago, Antonio; Trottier, H. D.; Wingate, M.; Aubin, C.; Bernard, C.; Burch, T.; DeTar, C.; Gottlieb, Steven; Gregory, E. B.; Heller, U. M.; Hetrick, J. E.; Osborn, J.; Sugar, R.; Toussaint, D.; Di Pierro,
1447:
as a framework for studying strongly coupled theories non-perturbatively. However, it was found to be a regularization suitable also for perturbative calculations. Perturbation theory involves an expansion in the coupling constant, and is well-justified in high-energy QCD where the coupling constant
1394:
Lattice QCD is a way to solve the theory exactly from first principles, without any assumptions, to the desired precision. However, in practice the calculation power is limited, which requires a smart use of the available resources. One needs to choose an action which gives the best physical
1403:
The quark masses are also approximated. Quark masses are larger than experimentally measured. These have been steadily approaching their physical values, and within the past few years a few collaborations have used nearly physical values to extrapolate down to physical
1448:
is small, while it fails completely when the coupling is large and higher order corrections are larger than lower orders in the perturbative series. In this region non-perturbative methods, such as Monte-Carlo sampling of the correlation function, are necessary.
1264:
can be used, in which the quark fields are treated as non-dynamic "frozen" variables. While this was common in early lattice QCD calculations, "dynamical" fermions are now standard. These simulations typically utilize algorithms based upon
1459:. In this case the lattice spacing is a real physical value, and not an artifact of the calculation which has to be removed (a UV regulator), and a quantum field theory can be formulated and solved on the physical lattice.
1395:
description of the system, with minimum errors, using the available computational power. The limited computer resources force one to use approximate physical constants which are different from their true physical values:
1221:
is the lattice spacing, which regularizes the theory. As a result, lattice QCD is mathematically well-defined. Most importantly, lattice QCD provides a framework for investigation of non-perturbative phenomena such as
2573:
1991:
M.; El-Khadra, A.; Kronfeld, A. S.; Mackenzie, P. B.; Menscher, D.; Simone, J. (2016). "BSMBench: A flexible and scalable HPC benchmark from beyond the standard model physics".
1432:
Lattice QCD Monte-Carlo calculations. In perturbative calculations both the operators of the action and the propagators are calculated on the lattice and expanded in powers of
1198:
of points in space and time. When the size of the lattice is taken infinitely large and its sites infinitesimally close to each other, the continuum QCD is recovered.
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Currently there is no formulation of lattice QCD that allows us to simulate the real-time dynamics of a quark-gluon system such as quarkâgluon plasma.
251:
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2095:
1440:, otherwise the results cannot be compared. The expansion has to be carried out to the same order in the continuum scheme and the lattice one.
1467:
The U(1), SU(2), and SU(3) lattice gauge theories can be reformulated into a form that can be simulated using "spin qubit manipulations" on a
2018:
1213:
at low energies. This formulation of QCD in discrete rather than continuous spacetime naturally introduces a momentum cut-off at the order 1/
1016:
1320:
Lattice QCD has also been used as a benchmark for high-performance computing, an approach originally developed in the context of the IBM
1295:
has been determined theoretically with an error of less than 2 percent. Lattice QCD predicts that the transition from confined quarks to
2697:
2215:
1151:
1436:. When renormalizing a calculation, the coefficients of the expansion need to be matched with a common continuum scheme, such as the
2692:
1379:
interaction part of the action to calculate the gauge configurations, and then uses the simulated gauge configurations to calculate
781:
1408:
In order to compensate for the errors one improves the lattice action in various ways, to minimize mainly finite spacing errors.
3376:
3133:
1607:; Trottier, H. D.; Wingate, M.; Aubin, C.; Bernard, C.; et al. (2004). "High-Precision Lattice QCD Confronts Experiment".
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A. Bazavov; et al. (2010). "Nonperturbative QCD simulations with 2+1 flavors of improved staggered quarks".
256:
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Byrnes, Tim; Yamamoto, Yoshihisa (17 February 2006). "Simulating lattice gauge theories on a quantum computer".
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Analytic or perturbative solutions in low-energy QCD are hard or impossible to obtain due to the highly
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33:
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S. DĂŒrr; Z. Fodor; J. Frison; et al. (2008). "Ab Initio
Determination of Light Hadron Masses".
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technique used to select the gauge configurations in the Monte-Carlo simulation imposes the use of
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Lattice QCD has already successfully agreed with many experiments. For example, the mass of the
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are free from the sign problem when applied to the case of QCD with gauge group SU(2) (QC
2065:
1966:
1917:
1909:
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In lattice QCD, fields representing quarks are defined at lattice sites (which leads to
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can be extremely computationally intensive, requiring the use of the largest available
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1993:
2016 International
Conference on High Performance Computing & Simulation (HPCS)
1493:
It provides reliable predictions only for hadrons containing heavy quarks, such as
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1051:
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83:
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2096:"ALICE collaboration opens avenue for high-precision studies of the strong force"
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17:
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2010:
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1276:
At present, lattice QCD is primarily applicable at low densities where the
2844:
2174:
Chandrasekharan, Wiese - An
Introduction to Chiral Symmetry on the Lattice
1371:, which depends on the action and the fields. Usually one starts with the
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3158:
2611:
2606:
2524:
2056:
716:
2200:
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2168:
2163:
1623:
3290:
3178:
3113:
3030:
3025:
2601:
1741:(1982). "Microcanonical Ensemble Formulation of Lattice Gauge Theory".
1494:
1456:
1376:
1340:
is a method to pseudo-randomly sample a large space of variables. The
1230:
formation, which are intractable by means of analytic field theories.
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2519:
2514:
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1957:
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2001:
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It is computationally intensive, with the bottleneck not being
1367:, using field configurations which are chosen according to the
2904:
1603:; Follana, E.; Gray, A.; Lepage, G. P.; Mason, Q.; Nobes, M.;
1455:
theory. One can use the lattice to represent the real atomic
1886:
P. Petreczky (2012). "Lattice QCD at non-zero temperature".
1359:
In lattice Monte-Carlo simulations the aim is to calculate
1451:
Lattice perturbation theory can also provide results for
2169:
Lombardo - Lattice QCD at Finite
Temperature and Density
2195:
1443:
The lattice regularization was initially introduced by
1245:
by repeated calculations at different lattice spacings
2183:
1785:"Lattice gauge theory in the microcanonical ensemble"
1260:. To reduce the computational burden, the so-called
3278:
3232:
3104:
3018:
2992:
2936:
2887:
2786:
2738:
2678:
2582:
2498:
2438:
2412:
2330:
2241:
1400:than wanted, leading to larger errors than wanted.
1317:), within the range of experimental measurements.
2860:
2216:
2184:The FermiQCD Library for Lattice Field theory
1363:. This is done by explicitly calculating the
1152:
8:
2179:Kuti, Julius - Lattice QCD and String Theory
2130:Introduction to Quantum Fields on a Lattice
1479:The method suffers from a few limitations:
2867:
2853:
2845:
2223:
2209:
2201:
2144:Lattice Methods for Quantum Chromodynamics
1159:
1145:
40:
29:
2055:
2000:
1974:
1956:
1899:
1838:
1694:
1676:
1674:
1622:
1252:Numerical lattice QCD calculations using
2137:Lattice Gauge Theories, An Introduction
1552:
1249:that are large enough to be tractable.
32:
1280:does not interfere with calculations.
2648:Inverse beta decay (electron capture)
2151:Quantum Chromodynamics on the Lattice
7:
1428:. The results are used primarily to
2164:Gupta - Introduction to Lattice QCD
1939:Rafelski, Johann (September 2015).
1490:but the bandwidth of memory access.
1416:In lattice perturbation theory the
27:Quantum chromodynamics on a lattice
2132:, Cambridge University Press 2002.
2122:, Cambridge University Press 1997.
2115:, Cambridge University Press 1985.
1424:in powers of the lattice spacing,
25:
1941:"Melting hadrons, boiling quarks"
1563:(1974). "Confinement of quarks".
2927:
2827:
2430:TolmanâOppenheimerâVolkoff limit
2321:
2196:Flavour Lattice Averaging Group
1945:The European Physical Journal A
1299:occurs around a temperature of
2149:C. Gattringer and C. B. Lang,
340:Renormalization group equation
1:
3316:Macroscopic quantum phenomena
1918:10.1088/0954-3899/39/9/093002
1641:10.1103/PhysRevLett.92.022001
1532:SU(2) color superconductivity
169:Spontaneous symmetry breaking
129:Symmetry in quantum mechanics
3326:Order and disorder (physics)
2715:Quantum chromodynamics (QCD)
2658:Electron degeneracy pressure
2120:Quantum Fields on a Lattice
2118:I. Montvay and G. MĂŒnster,
2113:Quarks, gluons and lattices
2011:10.1109/HPCSim.2016.7568421
1412:Lattice perturbation theory
1386:and correlation functions.
3393:
2074:10.1103/PhysRevA.73.022328
1976:10.1140/epja/i2015-15114-0
1763:10.1103/PhysRevLett.49.613
1713:10.1103/RevModPhys.82.1349
1469:universal quantum computer
1174:is a well-established non-
164:Explicit symmetry breaking
2925:
2822:
2663:Pauli exclusion principle
2363:Supernova nucleosynthesis
2319:
2296:Cataclysmic variable star
2142:T. DeGrand and C. DeTar,
1683:Reviews of Modern Physics
1497:, which have one or more
330:BargmannâWigner equations
257:Path Integral Formulation
3351:Thermo-dielectric effect
3250:Enthalpy of vaporization
2944:BoseâEinstein condensate
2619:Fundamental interactions
2146:, World Scientific 2006.
2139:, World Scientific 2005.
1812:10.1103/PhysRevD.28.1506
1587:10.1103/PhysRevD.10.2445
1194:formulated on a grid or
1178:approach to solving the
335:Schwinger-Dyson equation
3245:Enthalpy of sublimation
2705:Quantum electrodynamics
2311:Super soft X-ray source
1857:10.1126/science.1163233
1743:Physical Review Letters
1610:Physical Review Letters
1512:Lattice model (physics)
1390:Fermions on the lattice
1333:Monte-Carlo simulations
1271:microcanonical ensemble
365:Electroweak interaction
360:Quantum electrodynamics
325:WheelerâDeWitt equation
202:Background field method
3377:Quantum chromodynamics
3260:Latent internal energy
3010:Color-glass condensate
2814:Physics of shock waves
2574:Observational timeline
2420:Gravitational collapse
1278:numerical sign problem
1262:quenched approximation
1180:quantum chromodynamics
370:Quantum chromodynamics
227:Effective field theory
3070:Magnetically ordered
2710:Quantum hydrodynamics
1369:distribution function
1361:correlation functions
315:KleinâGordon equation
247:LSZ reduction formula
3372:Lattice field theory
2949:Fermionic condensate
2804:Nuclear astrophysics
2592:Elementary particles
1995:. pp. 834â839.
1777:David J. E. Callaway
1735:David J. E. Callaway
1522:Lattice gauge theory
1517:Lattice field theory
1192:lattice gauge theory
408:Theory of everything
242:Lattice field theory
212:Correlation function
34:Quantum field theory
3164:Chemical ionization
3056:Programmable matter
3046:Quantum spin liquid
2914:Supercritical fluid
2653:Degeneracy pressure
2583:Particles, forces,
2425:Chandrasekhar limit
2066:2006PhRvA..73b2328B
1967:2015EPJA...51..114R
1910:2012JPhG...39i3002P
1849:2008Sci...322.1224D
1804:1983PhRvD..28.1506C
1755:1982PhRvL..49..613C
1705:2010RvMP...82.1349B
1633:2004PhRvL..92b2001D
1579:1974PhRvD..10.2445W
1342:importance sampling
1282:Monte Carlo methods
1254:Monte Carlo methods
387:Incomplete theories
3311:Leidenfrost effect
3240:Enthalpy of fusion
3005:Quarkâgluon plasma
2809:Physical cosmology
2763:Quarkâgluon plasma
2624:Strong interaction
2189:2015-02-03 at the
1297:quarkâgluon plasma
1267:molecular dynamics
1228:quarkâgluon plasma
252:Partition function
179:Topological charge
99:General relativity
94:Special relativity
3359:
3358:
3341:Superheated vapor
3336:Superconductivity
3306:Equation of state
3154:Flash evaporation
3106:Phase transitions
3091:String-net liquid
2984:Photonic molecule
2954:Degenerate matter
2842:
2841:
2740:Degenerate matter
2725:Color confinement
2688:Quantum mechanics
2385:Carbon detonation
2331:Stellar processes
2044:Physical Review A
2020:978-1-5090-2088-1
1566:Physical Review D
1463:Quantum computing
1418:scattering matrix
1211:coupling constant
1169:
1168:
232:Expectation value
207:BRST quantization
154:Poincaré symmetry
109:YangâMills theory
89:Quantum mechanics
18:QCD lattice model
16:(Redirected from
3384:
3296:Compressed fluid
2931:
2876:States of matter
2869:
2862:
2855:
2846:
2834:Stars portal
2832:
2831:
2629:Weak interaction
2585:and interactions
2569:Electroweak star
2463:Pair instability
2380:Electron capture
2325:
2225:
2218:
2211:
2202:
2153:, Springer 2010.
2100:
2099:
2092:
2086:
2085:
2059:
2057:quant-ph/0510027
2039:
2033:
2032:
2004:
1987:
1981:
1980:
1978:
1960:
1936:
1930:
1929:
1903:
1883:
1877:
1876:
1842:
1833:(5905): 1224â7.
1822:
1816:
1815:
1798:(6): 1506â1514.
1789:
1773:
1767:
1766:
1731:
1725:
1724:
1698:
1689:(2): 1349â1417.
1678:
1669:
1668:
1626:
1601:Davies, C. T. H.
1597:
1591:
1590:
1557:
1453:condensed matter
1316:
1311:
1305:
1235:fermion doubling
1182:(QCD) theory of
1161:
1154:
1147:
222:Effective action
149:Lorentz symmetry
74:Electromagnetism
44:
30:
21:
3392:
3391:
3387:
3386:
3385:
3383:
3382:
3381:
3362:
3361:
3360:
3355:
3286:Baryonic matter
3274:
3228:
3199:Saturated fluid
3139:Crystallization
3100:
3074:Antiferromagnet
3014:
2988:
2932:
2923:
2883:
2873:
2843:
2838:
2826:
2818:
2782:
2734:
2674:
2643:Pair production
2584:
2578:
2552:Shell collapsar
2501:
2494:
2434:
2408:
2394:Gamma-ray burst
2374:Bondi accretion
2348:Nucleosynthesis
2326:
2317:
2276:Stellar physics
2237:
2229:
2191:Wayback Machine
2160:
2108:
2106:Further reading
2103:
2094:
2093:
2089:
2041:
2040:
2036:
2021:
1989:
1988:
1984:
1938:
1937:
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1885:
1884:
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1824:
1823:
1819:
1792:Physical Review
1787:
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1733:
1732:
1728:
1680:
1679:
1672:
1624:hep-lat/0304004
1599:
1598:
1594:
1559:
1558:
1554:
1550:
1508:
1477:
1465:
1414:
1392:
1375:part and gauge-
1335:
1330:
1324:supercomputer.
1309:
1307:
1300:
1287:
1165:
1136:
1135:
1134:
1132:
426:
418:
417:
413:Quantum gravity
388:
380:
379:
375:Higgs mechanism
355:
345:
344:
320:Proca equations
305:
297:
296:
292:Wightman Axioms
277:Renormalization
237:Feynman diagram
192:
184:
183:
124:
114:
113:
64:
49:
47:Feynman diagram
28:
23:
22:
15:
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11:
5:
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3272:
3267:
3265:Trouton's rule
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3146:
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3136:
3134:Critical point
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3116:
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3099:
3098:
3093:
3088:
3087:
3086:
3081:
3076:
3068:
3063:
3058:
3053:
3048:
3043:
3038:
3036:Liquid crystal
3033:
3028:
3022:
3020:
3016:
3015:
3013:
3012:
3007:
3002:
2996:
2994:
2990:
2989:
2987:
2986:
2981:
2976:
2971:
2969:Strange matter
2966:
2964:Rydberg matter
2961:
2956:
2951:
2946:
2940:
2938:
2934:
2933:
2926:
2924:
2922:
2921:
2916:
2911:
2902:
2897:
2891:
2889:
2885:
2884:
2874:
2872:
2871:
2864:
2857:
2849:
2840:
2839:
2837:
2836:
2823:
2820:
2819:
2817:
2816:
2811:
2806:
2801:
2796:
2790:
2788:
2787:Related topics
2784:
2783:
2781:
2780:
2778:Strange matter
2775:
2770:
2765:
2760:
2755:
2750:
2748:Neutron matter
2744:
2742:
2736:
2735:
2733:
2732:
2727:
2722:
2717:
2712:
2707:
2702:
2701:
2700:
2698:Basic concepts
2695:
2684:
2682:
2680:Quantum theory
2676:
2675:
2673:
2672:
2665:
2660:
2655:
2650:
2645:
2639:
2638:
2637:
2636:
2631:
2626:
2616:
2615:
2614:
2609:
2604:
2599:
2588:
2586:
2580:
2579:
2577:
2576:
2571:
2566:
2561:
2556:
2555:
2554:
2544:
2539:
2534:
2533:
2532:
2527:
2522:
2517:
2506:
2504:
2502:exotic objects
2496:
2495:
2493:
2492:
2485:
2480:
2475:
2470:
2465:
2460:
2455:
2453:Type Ib and Ic
2450:
2444:
2442:
2436:
2435:
2433:
2432:
2427:
2422:
2416:
2414:
2410:
2409:
2407:
2406:
2401:
2396:
2391:
2382:
2377:
2367:
2366:
2365:
2360:
2355:
2345:
2343:Surface fusion
2340:
2338:Nuclear fusion
2334:
2332:
2328:
2327:
2320:
2318:
2316:
2315:
2314:
2313:
2308:
2298:
2293:
2288:
2283:
2281:Stellar plasma
2278:
2273:
2268:
2263:
2258:
2253:
2247:
2245:
2239:
2238:
2230:
2228:
2227:
2220:
2213:
2205:
2199:
2198:
2193:
2181:
2176:
2171:
2166:
2159:
2158:External links
2156:
2155:
2154:
2147:
2140:
2133:
2123:
2116:
2107:
2104:
2102:
2101:
2087:
2034:
2019:
1982:
1931:
1878:
1817:
1781:Aneesur Rahman
1768:
1749:(9): 613â616.
1739:Aneesur Rahman
1726:
1670:
1605:Shigemitsu, J.
1592:
1551:
1549:
1546:
1545:
1544:
1539:
1534:
1529:
1524:
1519:
1514:
1507:
1504:
1503:
1502:
1499:strange quarks
1491:
1484:
1476:
1473:
1464:
1461:
1413:
1410:
1406:
1405:
1401:
1391:
1388:
1346:Euclidean time
1334:
1331:
1329:
1326:
1285:
1258:supercomputers
1209:and the large
1205:nature of the
1167:
1166:
1164:
1163:
1156:
1149:
1141:
1138:
1137:
1130:
1129:
1124:
1119:
1114:
1109:
1104:
1099:
1094:
1089:
1084:
1079:
1074:
1069:
1064:
1059:
1054:
1049:
1044:
1039:
1034:
1029:
1024:
1019:
1014:
1009:
1004:
999:
994:
989:
984:
979:
974:
969:
964:
959:
954:
949:
944:
939:
934:
929:
924:
919:
914:
909:
904:
899:
894:
889:
884:
879:
874:
869:
864:
859:
854:
849:
844:
839:
834:
829:
824:
819:
814:
809:
804:
799:
794:
789:
784:
779:
774:
769:
764:
759:
754:
749:
744:
739:
734:
729:
724:
719:
714:
709:
704:
699:
694:
689:
684:
679:
674:
669:
664:
659:
654:
649:
644:
639:
634:
629:
624:
619:
614:
609:
604:
599:
594:
589:
584:
579:
574:
569:
564:
559:
554:
549:
544:
539:
534:
529:
524:
519:
514:
509:
504:
499:
494:
489:
484:
479:
474:
469:
464:
459:
454:
449:
444:
439:
434:
428:
427:
424:
423:
420:
419:
416:
415:
410:
405:
400:
395:
389:
386:
385:
382:
381:
378:
377:
372:
367:
362:
356:
353:Standard Model
351:
350:
347:
346:
343:
342:
337:
332:
327:
322:
317:
312:
310:Dirac equation
306:
303:
302:
299:
298:
295:
294:
289:
287:Wick's theorem
284:
279:
274:
272:Regularization
269:
264:
259:
254:
249:
244:
239:
234:
229:
224:
219:
214:
209:
204:
199:
193:
190:
189:
186:
185:
182:
181:
176:
174:Noether charge
171:
166:
161:
159:Gauge symmetry
156:
151:
146:
141:
136:
131:
125:
120:
119:
116:
115:
112:
111:
106:
101:
96:
91:
86:
81:
76:
71:
65:
62:
61:
58:
57:
51:
50:
45:
37:
36:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
3389:
3378:
3375:
3373:
3370:
3369:
3367:
3352:
3349:
3347:
3344:
3342:
3339:
3337:
3334:
3332:
3329:
3327:
3324:
3322:
3321:Mpemba effect
3319:
3317:
3314:
3312:
3309:
3307:
3304:
3302:
3301:Cooling curve
3299:
3297:
3294:
3292:
3289:
3287:
3284:
3283:
3281:
3277:
3271:
3268:
3266:
3263:
3261:
3258:
3256:
3253:
3251:
3248:
3246:
3243:
3241:
3238:
3237:
3235:
3231:
3225:
3224:Vitrification
3222:
3220:
3217:
3215:
3212:
3210:
3207:
3205:
3202:
3200:
3197:
3195:
3192:
3190:
3189:Recombination
3187:
3185:
3184:Melting point
3182:
3180:
3177:
3175:
3172:
3170:
3167:
3165:
3162:
3160:
3157:
3155:
3152:
3150:
3147:
3145:
3142:
3140:
3137:
3135:
3132:
3130:
3129:Critical line
3127:
3125:
3122:
3120:
3119:Boiling point
3117:
3115:
3112:
3111:
3109:
3107:
3103:
3097:
3094:
3092:
3089:
3085:
3082:
3080:
3077:
3075:
3072:
3071:
3069:
3067:
3064:
3062:
3059:
3057:
3054:
3052:
3051:Exotic matter
3049:
3047:
3044:
3042:
3039:
3037:
3034:
3032:
3029:
3027:
3024:
3023:
3021:
3017:
3011:
3008:
3006:
3003:
3001:
2998:
2997:
2995:
2991:
2985:
2982:
2980:
2977:
2975:
2972:
2970:
2967:
2965:
2962:
2960:
2957:
2955:
2952:
2950:
2947:
2945:
2942:
2941:
2939:
2935:
2930:
2920:
2917:
2915:
2912:
2910:
2906:
2903:
2901:
2898:
2896:
2893:
2892:
2890:
2886:
2881:
2877:
2870:
2865:
2863:
2858:
2856:
2851:
2850:
2847:
2835:
2830:
2825:
2824:
2821:
2815:
2812:
2810:
2807:
2805:
2802:
2800:
2797:
2795:
2792:
2791:
2789:
2785:
2779:
2776:
2774:
2771:
2769:
2766:
2764:
2761:
2759:
2756:
2754:
2751:
2749:
2746:
2745:
2743:
2741:
2737:
2731:
2730:Deconfinement
2728:
2726:
2723:
2721:
2718:
2716:
2713:
2711:
2708:
2706:
2703:
2699:
2696:
2694:
2691:
2690:
2689:
2686:
2685:
2683:
2681:
2677:
2671:
2670:
2666:
2664:
2661:
2659:
2656:
2654:
2651:
2649:
2646:
2644:
2641:
2640:
2635:
2632:
2630:
2627:
2625:
2622:
2621:
2620:
2617:
2613:
2610:
2608:
2605:
2603:
2600:
2598:
2595:
2594:
2593:
2590:
2589:
2587:
2581:
2575:
2572:
2570:
2567:
2565:
2562:
2560:
2557:
2553:
2550:
2549:
2548:
2545:
2543:
2540:
2538:
2535:
2531:
2528:
2526:
2523:
2521:
2518:
2516:
2513:
2512:
2511:
2508:
2507:
2505:
2503:
2497:
2491:
2490:
2486:
2484:
2481:
2479:
2476:
2474:
2471:
2469:
2466:
2464:
2461:
2459:
2456:
2454:
2451:
2449:
2446:
2445:
2443:
2441:
2437:
2431:
2428:
2426:
2423:
2421:
2418:
2417:
2415:
2411:
2405:
2404:Orbital decay
2402:
2400:
2397:
2395:
2392:
2390:
2386:
2383:
2381:
2378:
2375:
2371:
2368:
2364:
2361:
2359:
2356:
2354:
2351:
2350:
2349:
2346:
2344:
2341:
2339:
2336:
2335:
2333:
2329:
2324:
2312:
2309:
2307:
2304:
2303:
2302:
2299:
2297:
2294:
2292:
2291:Variable star
2289:
2287:
2284:
2282:
2279:
2277:
2274:
2272:
2269:
2267:
2264:
2262:
2259:
2257:
2254:
2252:
2249:
2248:
2246:
2244:
2240:
2236:
2233:
2226:
2221:
2219:
2214:
2212:
2207:
2206:
2203:
2197:
2194:
2192:
2188:
2185:
2182:
2180:
2177:
2175:
2172:
2170:
2167:
2165:
2162:
2161:
2157:
2152:
2148:
2145:
2141:
2138:
2134:
2131:
2127:
2124:
2121:
2117:
2114:
2110:
2109:
2105:
2098:. 2020-12-09.
2097:
2091:
2088:
2083:
2079:
2075:
2071:
2067:
2063:
2058:
2053:
2050:(2): 022328.
2049:
2045:
2038:
2035:
2030:
2026:
2022:
2016:
2012:
2008:
2003:
1998:
1994:
1986:
1983:
1977:
1972:
1968:
1964:
1959:
1954:
1950:
1946:
1942:
1935:
1932:
1927:
1923:
1919:
1915:
1911:
1907:
1902:
1897:
1894:(9): 093002.
1893:
1889:
1882:
1879:
1874:
1870:
1866:
1862:
1858:
1854:
1850:
1846:
1841:
1836:
1832:
1828:
1821:
1818:
1813:
1809:
1805:
1801:
1797:
1793:
1786:
1782:
1778:
1772:
1769:
1764:
1760:
1756:
1752:
1748:
1744:
1740:
1736:
1730:
1727:
1722:
1718:
1714:
1710:
1706:
1702:
1697:
1692:
1688:
1684:
1677:
1675:
1671:
1666:
1662:
1658:
1654:
1650:
1646:
1642:
1638:
1634:
1630:
1625:
1620:
1617:(2): 022001.
1616:
1612:
1611:
1606:
1602:
1596:
1593:
1588:
1584:
1580:
1576:
1572:
1568:
1567:
1562:
1556:
1553:
1547:
1543:
1542:Wilson action
1540:
1538:
1537:QCD sum rules
1535:
1533:
1530:
1528:
1525:
1523:
1520:
1518:
1515:
1513:
1510:
1509:
1505:
1500:
1496:
1492:
1489:
1485:
1482:
1481:
1480:
1474:
1472:
1470:
1462:
1460:
1458:
1454:
1449:
1446:
1441:
1439:
1438:MS-bar scheme
1435:
1431:
1427:
1423:
1419:
1411:
1409:
1402:
1398:
1397:
1396:
1389:
1387:
1385:
1382:
1378:
1374:
1370:
1366:
1362:
1357:
1355:
1351:
1350:Wick rotation
1347:
1343:
1339:
1332:
1327:
1325:
1323:
1318:
1315:
1304:
1298:
1294:
1289:
1283:
1279:
1274:
1272:
1268:
1263:
1259:
1255:
1250:
1248:
1244:
1240:
1236:
1231:
1229:
1225:
1220:
1216:
1212:
1208:
1204:
1199:
1197:
1193:
1189:
1185:
1181:
1177:
1173:
1162:
1157:
1155:
1150:
1148:
1143:
1142:
1140:
1139:
1133:
1128:
1125:
1123:
1120:
1118:
1115:
1113:
1110:
1108:
1105:
1103:
1102:Zamolodchikov
1100:
1098:
1097:Zamolodchikov
1095:
1093:
1090:
1088:
1085:
1083:
1080:
1078:
1075:
1073:
1070:
1068:
1065:
1063:
1060:
1058:
1055:
1053:
1050:
1048:
1045:
1043:
1040:
1038:
1035:
1033:
1030:
1028:
1025:
1023:
1020:
1018:
1015:
1013:
1010:
1008:
1005:
1003:
1000:
998:
995:
993:
990:
988:
985:
983:
980:
978:
975:
973:
970:
968:
965:
963:
960:
958:
955:
953:
950:
948:
945:
943:
940:
938:
935:
933:
930:
928:
925:
923:
920:
918:
915:
913:
910:
908:
905:
903:
900:
898:
895:
893:
890:
888:
885:
883:
880:
878:
875:
873:
870:
868:
865:
863:
860:
858:
855:
853:
850:
848:
845:
843:
840:
838:
835:
833:
830:
828:
825:
823:
820:
818:
815:
813:
810:
808:
805:
803:
800:
798:
795:
793:
790:
788:
785:
783:
780:
778:
775:
773:
770:
768:
765:
763:
760:
758:
755:
753:
750:
748:
745:
743:
740:
738:
735:
733:
730:
728:
725:
723:
720:
718:
715:
713:
710:
708:
705:
703:
700:
698:
695:
693:
690:
688:
685:
683:
680:
678:
675:
673:
670:
668:
665:
663:
660:
658:
655:
653:
650:
648:
645:
643:
640:
638:
635:
633:
630:
628:
625:
623:
620:
618:
615:
613:
610:
608:
605:
603:
600:
598:
595:
593:
590:
588:
585:
583:
580:
578:
575:
573:
570:
568:
565:
563:
560:
558:
555:
553:
550:
548:
545:
543:
540:
538:
535:
533:
530:
528:
525:
523:
520:
518:
515:
513:
510:
508:
505:
503:
500:
498:
495:
493:
490:
488:
485:
483:
480:
478:
475:
473:
470:
468:
465:
463:
460:
458:
455:
453:
450:
448:
445:
443:
440:
438:
435:
433:
430:
429:
422:
421:
414:
411:
409:
406:
404:
401:
399:
398:Supersymmetry
396:
394:
393:String theory
391:
390:
384:
383:
376:
373:
371:
368:
366:
363:
361:
358:
357:
354:
349:
348:
341:
338:
336:
333:
331:
328:
326:
323:
321:
318:
316:
313:
311:
308:
307:
301:
300:
293:
290:
288:
285:
283:
280:
278:
275:
273:
270:
268:
265:
263:
260:
258:
255:
253:
250:
248:
245:
243:
240:
238:
235:
233:
230:
228:
225:
223:
220:
218:
215:
213:
210:
208:
205:
203:
200:
198:
195:
194:
188:
187:
180:
177:
175:
172:
170:
167:
165:
162:
160:
157:
155:
152:
150:
147:
145:
142:
140:
137:
135:
132:
130:
127:
126:
123:
118:
117:
110:
107:
105:
102:
100:
97:
95:
92:
90:
87:
85:
82:
80:
77:
75:
72:
70:
67:
66:
60:
59:
56:
53:
52:
48:
43:
39:
38:
35:
31:
19:
3346:Superheating
3219:Vaporization
3214:Triple point
3209:Supercooling
3174:Lambda point
3124:Condensation
3041:Time crystal
3019:Other states
2959:Quantum Hall
2799:Astrophysics
2768:Preon matter
2758:Quark matter
2719:
2693:Introduction
2667:
2510:Neutron star
2500:Compact and
2487:
2399:Helium flash
2389:deflagration
2306:X-ray binary
2232:Stellar core
2150:
2143:
2136:
2129:
2119:
2112:
2090:
2047:
2043:
2037:
1992:
1985:
1948:
1944:
1934:
1891:
1887:
1881:
1830:
1826:
1820:
1795:
1791:
1771:
1746:
1742:
1729:
1686:
1682:
1614:
1608:
1595:
1570:
1564:
1555:
1478:
1466:
1450:
1442:
1433:
1425:
1415:
1407:
1393:
1373:gauge bosons
1358:
1336:
1319:
1290:
1275:
1273:algorithms.
1251:
1246:
1242:
1239:extrapolated
1232:
1218:
1214:
1207:strong force
1200:
1176:perturbative
1171:
1170:
1131:
977:Stueckelberg
707:Jona-Lasinio
282:Vacuum state
267:Quantization
104:Gauge theory
84:Strong force
69:Field theory
3255:Latent heat
3204:Sublimation
3149:Evaporation
3084:Ferromagnet
3079:Ferrimagnet
3061:Dark matter
2993:High energy
2720:Lattice QCD
2634:Gravitation
2559:Exotic star
2537:White dwarf
2530:Radio-quiet
2301:Binary star
2271:Metallicity
2111:M. Creutz,
1573:(8): 2445.
1475:Limitations
1430:renormalize
1384:propagators
1338:Monte-Carlo
1224:confinement
1172:Lattice QCD
1117:Zinn-Justin
967:Sommerfield
892:Pomeranchuk
857:Osterwalder
852:Oppenheimer
782:ĆopuszaĆski
602:Fredenhagen
403:Technicolor
3366:Categories
3270:Volatility
3233:Quantities
3194:Regelation
3169:Ionization
3144:Deposition
3096:Superglass
3066:Antimatter
3000:QCD matter
2979:Supersolid
2974:Superfluid
2937:Low energy
2773:Strangelet
2753:QCD matter
2564:Quark star
2542:Black hole
2473:Quark-nova
2440:Supernovae
2358:RP-process
2286:Supergiant
2135:H. Rothe,
1958:1508.03260
1951:(9): 114.
1888:J. Phys. G
1561:Wilson, K.
1548:References
1527:QCD matter
1328:Techniques
1190:. It is a
1112:Zimmermann
1007:Vainshtein
882:Polchinski
742:Kontsevich
687:Iliopoulos
662:Heisenberg
487:Bogoliubov
425:Scientists
262:Propagator
144:T-symmetry
139:P-symmetry
134:C-symmetry
122:Symmetries
79:Weak force
63:Background
2794:Astronomy
2547:Collapsar
2468:Hypernova
2370:Accretion
2353:R-process
2261:Structure
2256:Evolution
2251:Formation
2029:115229961
2002:1401.3733
1926:119193093
1901:1203.5320
1840:0906.3599
1721:119259340
1696:0903.3598
1649:0031-9007
1354:spacetime
1322:Blue Gene
1301:150
1203:nonlinear
1047:Wetterich
1032:Weisskopf
982:Sudarshan
932:Schwinger
842:Nishijima
807:Maldacena
772:Leutwyler
732:Kinoshita
632:Goldstone
622:Gell-Mann
537:Doplicher
304:Equations
3331:Spinodal
3279:Concepts
3159:Freezing
2612:Neutrino
2607:Electron
2525:Magnetar
2413:Collapse
2235:collapse
2187:Archived
1873:14225402
1865:19023076
1783:(1983).
1665:16205350
1657:14753930
1506:See also
1495:hyperons
1422:expanded
1381:hadronic
1312:10
1217:, where
1062:Wightman
1027:Weinberg
1017:Virasoro
997:Tomonaga
992:Thirring
987:Symanzik
947:Semenoff
922:Schrader
887:Polyakov
802:Majorana
737:Klebanov
692:Ivanenko
682:'t Hooft
652:Guralnik
597:Fröhlich
592:Fritzsch
587:Frampton
502:Buchholz
447:Bargmann
437:Anderson
217:Crossing
3291:Binodal
3179:Melting
3114:Boiling
3031:Crystal
3026:Colloid
2669:More...
2602:Neutron
2489:More...
2483:Remnant
2458:Type II
2448:Type Ia
2126:J. Smit
2082:6105195
2062:Bibcode
1963:Bibcode
1906:Bibcode
1845:Bibcode
1827:Science
1800:Bibcode
1751:Bibcode
1701:Bibcode
1629:Bibcode
1575:Bibcode
1457:crystal
1404:values.
1377:fermion
1348:, by a
1196:lattice
1072:Wilczek
1037:Wentzel
1012:Veltman
957:Shirkov
952:Shifman
942:Seiberg
927:Schwarz
907:Rubakov
827:Naimark
777:Lipatov
767:Lehmann
747:Kreimer
727:Kendall
617:Gelfand
612:Glashow
572:Feynman
552:Faddeev
547:Englert
517:Coleman
507:Cachazo
492:Brodsky
477:Bjorken
467:Berezin
457:Belavin
197:Anomaly
55:History
2919:Plasma
2900:Liquid
2597:Proton
2520:Quasar
2515:Pulsar
2478:Nebula
2080:
2027:
2017:
1924:
1871:
1863:
1719:
1663:
1655:
1647:
1445:Wilson
1365:action
1293:proton
1188:gluons
1184:quarks
1127:Zumino
1092:Yukawa
1082:Witten
1077:Wilson
1067:Wigner
1002:Tyutin
962:Skyrme
912:Ruelle
877:Plefka
872:Peskin
862:Parisi
822:MĂžller
812:Migdal
797:Maiani
792:LĂŒders
757:Landau
752:Kuraev
722:KÀllén
712:Jordan
697:Jackiw
637:Gribov
527:DeWitt
522:Dashen
512:Callan
482:Bleuer
452:Becchi
442:Anselm
2909:Vapor
2895:Solid
2888:State
2243:Stars
2078:S2CID
2052:arXiv
2025:S2CID
1997:arXiv
1953:arXiv
1922:S2CID
1896:arXiv
1869:S2CID
1835:arXiv
1788:(PDF)
1717:S2CID
1691:arXiv
1661:S2CID
1619:arXiv
1488:flops
1243:a = 0
1122:Zuber
972:Stora
937:Segal
917:Salam
902:Proca
897:Popov
867:Pauli
847:Oehme
837:Neveu
832:Nambu
817:Mills
702:Jaffe
677:Hagen
672:Higgs
647:Gupta
642:Gross
627:Glimm
607:Furry
577:Fierz
567:Fermi
562:Fayet
557:Fadin
542:Dyson
532:Dirac
497:Brout
472:Bethe
432:Adler
191:Tools
2880:list
2266:Core
2015:ISBN
1861:PMID
1779:and
1737:and
1653:PMID
1645:ISSN
1288:D).
1226:and
1186:and
1087:Yang
1057:Wick
1052:Weyl
1042:Wess
1022:Ward
717:Jost
667:Hepp
657:Haag
582:Fock
462:Bell
2905:Gas
2070:doi
2007:doi
1971:doi
1914:doi
1853:doi
1831:322
1808:doi
1796:D28
1759:doi
1709:doi
1637:doi
1583:doi
1420:is
1352:of
1308:1.7
1303:MeV
1269:or
1241:to
1107:Zee
787:Low
762:Lee
3368::
2907:/
2387:/
2128:,
2076:.
2068:.
2060:.
2048:73
2046:.
2023:.
2013:.
2005:.
1969:.
1961:.
1949:51
1947:.
1943:.
1920:.
1912:.
1904:.
1892:39
1890:.
1867:.
1859:.
1851:.
1843:.
1829:.
1806:.
1794:.
1790:.
1757:.
1747:49
1745:.
1715:.
1707:.
1699:.
1687:82
1685:.
1673:^
1659:.
1651:.
1643:.
1635:.
1627:.
1615:92
1613:.
1581:.
1571:10
1569:.
1471:.
1356:.
2882:)
2878:(
2868:e
2861:t
2854:v
2376:)
2372:(
2224:e
2217:t
2210:v
2084:.
2072::
2064::
2054::
2031:.
2009::
1999::
1979:.
1973::
1965::
1955::
1928:.
1916::
1908::
1898::
1875:.
1855::
1847::
1837::
1814:.
1810::
1802::
1765:.
1761::
1753::
1723:.
1711::
1703::
1693::
1667:.
1639::
1631::
1621::
1589:.
1585::
1577::
1501:.
1434:a
1426:a
1314:K
1310:Ă
1306:(
1286:2
1247:a
1219:a
1215:a
1160:e
1153:t
1146:v
20:)
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