Finite-size behavior near the critical point of QCD phase-transition

CHEN Li-Zhu; CHEN Yun-Yun; WU Yuan-Fang

doi:10.1088/1674-1137/38/10/104103

Chinese Physics C> 2014, Vol. 38> Issue(10) : 104103 DOI: 10.1088/1674-1137/38/10/104103

Finite-size behavior near the critical point of QCD phase-transition

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Abstract：
It is pointed out that the finite-size effect is not negligible in locating the critical point of quantum colordynamics (QCD) phase transitions at current relativistic heavy ion collisions. The finite-size scaling form of the critical related observable is suggested. Its fixed point behavior at critical incident energy can be served as a reliable identification of a critical point and nearby boundary of QCD phase transition. How to experimentally find the fixed point behavior is demonstrated by using 3D-Ising model as an example. The validity of the method at finite detector acceptances at RHIC is also discussed.

References

[1]

Collins J C, Perry M J. Phys. Rev. Lett., 1975, 34: 1353; Freedman B A, Lerran L D. Phys. Rev. D, 1977, 16: 1196; Shuryak E V, Phys. Lett. B, 1981, 107: 103[2] Aoki Y, Endrodi G, Fodor Z et al. Nature, 2006, 443: 675; Aoki Y, Fodor Z, Katz S D et al. Phys. Lett. B, 2006, 643: 46[3] Fodor Z, Katz S D. JHEP, 2004, 04: 050; Fodor Z, Katz S D, Szabo K K. Phys. Lett. B, 2003, 568: 73[4] Gyulassy M, McLerran L. Nucl. Phys. A, 2005, 750: 30-63; Adams J et al. (STAR collaboration). Nucl. Phys. A, 2005, 757: 102[5] Stephanov M A. Int. J. Mod. Phys. A, 2005, 20: 4387[6] Stephanov M A. Phys. Rev. Lett., 2009, 102: 032301[7] Asakawa M, Ejiri S, Kitazawa M. Phys. Rev. Lett., 2009, 103: 262301[8] Weber C, Capriotti L, Misguich G et al. Phys. Rev. Lett., 2003, 91: 177202[9] Olsson P. Phys. Rev. B, 1997, 55: 3583[10] Adams J et al. (STAR collaboration). Phys. Rev. Lett., 2004, 93: 012301; Adler S S et al. (PHENIX collaboration). Phys. Rev. Lett., 2004, 93: 152302; Soltz R A. J. Phys. G: Nucl. Part. Phys., 2005, 31: S325[11] Stephanov M A, Rajagopal K, Shuryak E. Phys. Rev. D, 1999, 60: 114028[12] Antoniou N G, Diakonos F K, Kapoyannis A S. Phys. Rev. Lett., 2006, 97: 032002[13] Berdnikov B, Rajagopal K. Phys. Rev. D, 2000, 61: 105017[14] Paech K. Eur. Phys. J. C, 2004, 33: S627[15] Rajagopal K, Wilczek F. Nucl. Phys. B, 1993, 399: 395[16] Stephanov M A, Rajagopal K, Shuyak E. Phys. Rev. Lett., 1998, 81: 4816; Heiselberg H. Phys. Rept., 2001, 351: 161[17] Stephanov M A. Phys. Rev. Lett., 2009, 102: 032301; Masayuki Asakawa, Shinji Ejiri, Masakiyo Kitazawa. arXiv: nuclth/0904.2089[18] Fisher M E. in Critical Phenomena. Proceedings of the International School of Physics Enrico Fermi, Course 51, edited by Green M S (Academic, New York, 1971)[19] Brézin E. J. Phys., 1982, 43: 15[20] CHEN X S, Dohm V, Talapov A L. Physica A, 1996, 232: 375; CHEN X S, Dohm V, Schultka N. Phys. Rev. Lett., 1996, 77: 641[21] Berkenbusch M K, Bauer W, Dillman K et al. Phys. Rev. Lett., 2001, 88: 022701[22] Binder K. Rep. Prog. Phys., 1987, 50: 783[23] van Leeuwen J M J. Phys. Rev. Lett., 1975, 34: 1056; Nienhuis B, Nauenberg M. 1975, 35: 477; Fisher M E, Berker A N. Phys. Rev. B, 1982, 26: 2507[24] Binder K, Landau D P. Phys. Rev. B, 1984, 30: 1477[25] Ukawa A. Lecture on Lattice QCD at finite temperature (1993)[26] Cleymans J, Oeschler H, Redlich K et al. Phys. Rev. C, 2006, 73: 034905[27] Jeon S, Koch V. Phys. Rev. Lett., 2000, 85: 2076; Koch V. arXiv: nuclth/0810.2520[28] Adams J et al. (STAR collaboration). Phys. Rev. C, 2005, 72: 044902; Abelev B I et al. (STAR collaboration). Phys. Rev. C, 2009, 79: 024906[29] Garcá J, Gonzalo J A. Physica A, 2003, 326: 464[30] Binder K. Z. Phys. B, 1981, 43: 119[31] Asakawa M J. Phys. G: Nucl. Part. Phys, 2009, 36: 064042; Philippe de Forcrand, Owe Philipsen. Phys. Rev. Lett, 2010, 105: 152001; Stephanov M A. arXiv: hepth/0402115; Rchr J J, Mcrmin N D. Phys. Rev. A, 1973 8: 472; Nigel B Wilding. J. Phys.: Condens. Matter, 1997, 9: 585; Nonaka C, Asakawa M. Phys. Rev. C, 2005, 71: 044904; PAN Xue, CHEN Li-Zhu, CHEN Xiao-Song et al. Nucl. Phys. A, 2013, 913: 206

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[20]	Wu Chongshi , Zeng Jinyan . Nuclear Pairing Phase Transition. Chinese Physics C, 1988, 12(S1): 81-90.

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CHEN Li-Zhu, CHEN Yun-Yun and WU Yuan-Fang. Finite-size behavior near the critical point of QCD phase-transition[J]. Chinese Physics C, 2014, 38(10): 104103. doi: 10.1088/1674-1137/38/10/104103

CHEN Li-Zhu, CHEN Yun-Yun and WU Yuan-Fang. Finite-size behavior near the critical point of QCD phase-transition[J]. Chinese Physics C, 2014, 38(10): 104103. doi: 10.1088/1674-1137/38/10/104103 shu

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Received: 2013-11-19
Revised: 2014-04-11

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沈阳化工大学材料科学与工程学院沈阳 110142

Finite-size behavior near the critical point of QCD phase-transition

Corresponding author: CHEN Li-Zhu,

Received Date: 2013-11-19

Accepted Date: 2014-04-11

Available Online: 2014-10-05

Abstract: It is pointed out that the finite-size effect is not negligible in locating the critical point of quantum colordynamics (QCD) phase transitions at current relativistic heavy ion collisions. The finite-size scaling form of the critical related observable is suggested. Its fixed point behavior at critical incident energy can be served as a reliable identification of a critical point and nearby boundary of QCD phase transition. How to experimentally find the fixed point behavior is demonstrated by using 3D-Ising model as an example. The validity of the method at finite detector acceptances at RHIC is also discussed.

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Finite-size behavior near the critical point of QCD phase-transition

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