Behavior and finite-size effects of the sixth order cumulant in the three-dimensional Ising universality class

Xue Pan; Li-Zhu Chen; Yuan-Fang Wu

doi:10.1088/1674-1137/40/9/093104

Chinese Physics C> 2016, Vol. 40> Issue(9) : 093104 DOI: 10.1088/1674-1137/40/9/093104

Behavior and finite-size effects of the sixth order cumulant in the three-dimensional Ising universality class

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Abstract：
The high-order cumulants of conserved charges are suggested to be sensitive observables to search for the critical point of Quantum Chromodynamics (QCD). This has been calculated to the sixth order in experiments. Corresponding theoretical studies on the sixth order cumulant are necessary. Based on the universality of the critical behavior, we study the temperature dependence of the sixth order cumulant of the order parameter using the parametric representation of the three-dimensional Ising model, which is expected to be in the same universality class as QCD. The density plot of the sign of the sixth order cumulant is shown on the temperature and external magnetic field plane. We found that at non-zero external magnetic field, when the critical point is approached from the crossover side, the sixth order cumulant has a negative valley. The width of the negative valley narrows with decreasing external field. Qualitatively, the trend is similar to the result of Monte Carlo simulation on a finite-size system. Quantitatively, the temperature of the sign change is different. Through Monte Carlo simulation of the Ising model, we calculated the sixth order cumulant of different sizes of systems. We discuss the finite-size effects on the temperature at which the cumulant changes sign.
- critical point ,
- the sixth order cumulant ,
- Ising model

References

[1]	L. G. Yaffe and B. Svetitsky, Phys. Rev. D, 26:963(1982)
[2]	A. Roberge and N. Weiss, Nucl. Phys. B, 27:5734(1986)
[3]	M. Fukugita, M. Okawa, and A. Ukawa, Phys. Rev. Lett., 63:1768(1989)
[4]	P. de Forcrand and O. Philipsen, Nucl. Phys. B, 64:2290(2002)
[5]	S. Ejiri, Phys. Rev. D, 78:074507(2008)
[6]	E. S. Bowman and J. I. Kapusta, Phys. Rev. C, 79:015202(2009)
[7]	Y. Aoki, G. Endrdi, Z. Fodor et al, Nature, 443:675(2006)
[8]	M. E. Fisher, and A. E. Ferdinand, Phys. Rev. Lett., 49:169(1967)
[9]	M. S. S. Challa, D. P. Landau, and K. Binder, Phys. Rev. B, 34:1841(1986)
[10]	M. A. Stephanov, K. Rajagopal, and E. V. Shuryak, Phys. Rev. D, 60:114028(1999)
[11]	B. Berdnikov and K. Rajagopal, Phys. Rev. D, 61:105017(2000)
[12]	Y. Hatta and M. A. Stephanov, Phys. Rev. Lett., 91:102003(2003)
[13]	V. Koch, arXiv:0810.2520
[14]	M. A. Stephanov, Phys. Rev. Lett., 102:032301(2009)
[15]	M. Asakawa, S. Ejiri, and M. Kitazawa, Phys. Rev. Lett., 103:262301(2009)
[16]	M. A. Stephanov, Phys. Rev. Lett., 107:052301(2001)
[17]	B. Friman, F. Karsch, K. Redlich et al, Eur. Phys. J. C, 71:1694(2001)
[18]	M. Cheng, P. Hegde, C. Jung et al, Phys. Rev. D, 79:074505(2009)
[19]	Wei-jie Fu, Yu-Xin Liu, and Yue-Liang Wu, Phys. Rev. D, 81:014028(2010)
[20]	V. Skokov, B. Stokić, B. Friman et al, Phys. Rev. C, 82:015206(2010)
[21]	V. Skokov, B. Friman, and K. Redlich, Phys. Rev. C, 83:054904(2011)
[22]	V. Skokov, B. Friman, E. Nakano et al, Phys. Rev. D, 82:034029(2010)
[23]	M. M. Aggarwal et al (STAR Collaboration), Phys. Rev. Lett., 105:22302(2010)
[24]	F. Karsch and K. Redlich, Phys. Lett. B, 695:136(2011)
[25]	Li-Zhu Chen, Nucl. Phys. A, 904:471c (2013)
[26]	P. de Forcrand and O. Philipsen, Phys. Rev. Lett., 105:152001(2010)
[27]	M. Stephanov, K. Rajagopal, and E. Shuryak, Phys. Rev. Lett., 81:4816(1998)
[28]	M. Asakawa, J. Phys. G:Nucl. Part. Phys, 36:064042(2009)
[29]	R. D. Pisarski, F. Wilczek, Phys. Rev. D, 29:338(1984)
[30]	Xue Pan, Li-Zhu Chen, X. S. Chen, and Yuan-Fang Wu, Nucl. Phys. A, 913:206(2013)
[31]	L. F. Palhares, E. S. Fraga, and T. Kodama, J. Phys. G:Nucl. Part. Phys, 37:094031(2010)
[32]	L. F. Palhares, E. S. Fraga, and T. Kodama, J. Phys. G:Nucl. Part. Phys, 38:085101(2011)
[33]	J. Braun, B. Klein, and B. J. Schaefer, Phys. Lett. B, 713:216(2012)
[34]	R. A. Tripolt, J. Braun, B. Klein et al, Phys. Rev. D, 90:054012(2014)
[35]	P. Schofield, Phys. Rev. Lett., 22:606(1969)
[36]	D. J. Wallace and R. K. P. Zia, J. Phys. C:Solid State Phys, 7:3480(1974)
[37]	H. W. J. Blte, E. Luijten, and J. R. Heringa, J. Phys. A:Math. Gen, 28:6289(1995)
[38]	B. D. Josephson and J. Phys. C:Solid State Phys, 2:113(1969)
[39]	J. Engels, L. Fromme, and M. Seniuch, Nucl. Phys. B, 655:277(2003)
[40]	U. Wolff, Phys. Rev. Lett., 62:361(1989)
[41]	V. Privman, Finite Size Scaling and Numerical Simulation of Statistical Physics, First edition (Farrer Road, Singapore:World Scientific Publishing Co. Pte. Ltd., 1990), p.11

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[15]	LIU Jun , SHEN Yang , LUO Xiang-Qian . Parallel Computing of the Ising Model. Chinese Physics C, 2004, 28(2): 122-128.
[16]	Xing Yongzhong , Xu Gongou . On Ground-State Correlation in Nuclear Many-Body Systems. Chinese Physics C, 1997, 21(S4): 79-86.
[17]	Zhang Jun , Yang Guangcan , Yan Hong . Two Dimensional Cyclic Representations of U_q(sl₂)and 8-Vertex Ising Model. Chinese Physics C, 1995, 19(11): 1005-1011.
[18]	Zheng Xite , Lei Chunhong , Li Yuliang , Chen Hong . Study of Higher Order Cumulant Expansion of U(l) Lattice Gauge Model at Finite Temperature. Chinese Physics C, 1993, 17(S3): 271-276.
[19]	WEN Jia-Ru , HUANG Tao . BARYONS AS SOLITONS IN A NON-LINEAR σ MODEL WITH ONLY A SIXTH-ORDER STABILIZING TERM. Chinese Physics C, 1988, 12(2): 286-288.
[20]	Wen Jiaru , Huang Tao . Baryons as Solitons in a Non-Linear a Model With Only a Sixth-Order Stabilizing Term. Chinese Physics C, 1988, 12(S1): 77-80.

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Xue Pan, Li-Zhu Chen and Yuan-Fang Wu. Behavior and finite-size effects of the sixth order cumulant in the three-dimensional Ising universality class[J]. Chinese Physics C, 2016, 40(9): 093104. doi: 10.1088/1674-1137/40/9/093104

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Received: 2016-04-29
Revised: 2016-05-17

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Supported by Fund Project of Sichuan Provincial Department of Education (16ZB0339), Fund Project of Chengdu Technological University for Doctor (2016RC004), Major State Basic Research Development Program of China (2014CB845402) and National Natural Science Foundation of China (11405088, 11221504)

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沈阳化工大学材料科学与工程学院沈阳 110142

Behavior and finite-size effects of the sixth order cumulant in the three-dimensional Ising universality class

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Behavior and finite-size effects of the sixth order cumulant in the three-dimensional Ising universality class

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