Finite-size behaviour of generalized susceptibilities in the whole phase plane of the Potts model

Xue Pan; Yanhua Zhang; Lizhu Chen; Mingmei Xu; Yuanfang Wu

doi:10.1088/1674-1137/42/2/023110

Chinese Physics C> 2018, Vol. 42> Issue(2) : 023110 DOI: 10.1088/1674-1137/42/2/023110

Finite-size behaviour of generalized susceptibilities in the whole phase plane of the Potts model

Xue Pan ^1,2,, ,
Yanhua Zhang ² ,
Lizhu Chen ³ ,
Mingmei Xu ² ,
Yuanfang Wu ²

1.
School of Electronic Engineering, Chengdu Technological University, Chengdu 611730, China
2.
Key Laboratory of Quark and Lepton Physics(MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079, China
3.
Key Laboratory of Quark and Lepton Physics(MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079, China
4.
School of Physics and Optoelectronic Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, China

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Abstract：
We study the sign distribution of generalized magnetic susceptibilities in the temperature-external magnetic field plane using the three-dimensional three-state Potts model. We find that the sign of odd-order susceptibility is opposite in the symmetric (disorder) and broken (order) phases, but that of the even-order one remains positive when it is far away from the phase boundary. When the critical point is approached from the crossover side, negative fourth-order magnetic susceptibility is observable. It is also demonstrated that non-monotonic behavior occurs in the temperature dependence of the generalized susceptibilities of the energy. The finite-size scaling behavior of the specific heat in this model is mainly controlled by the critical exponent of the magnetic susceptibility in the three-dimensional Ising universality class.
- Potts model ,
- critical point ,
- generalized susceptibilities

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[1]	J. Adams et al (STAR Collaboration), Nucl. Phys. A, 757:102 (2005)
[2]	P. de Forcrand and O. Philipsen, Nucl. Phys. B, 642:290 (2002)
[3]	S. Ejiri, Phys. Rev. D, 78:074507 (2008)
[4]	E. S. Bowman and J. I. Kapusta, Phys. Rev. C, 79:015202 (2009)
[5]	M. Stephanov, K. Rajagopal, and E. Shuryak, Phys. Rev. Lett., 81:4816 (1998)
[6]	P. de Forcrand and O. Philipsen, Phys. Rev. Lett., 105:152001 (2010)
[7]	Bazavov A, Ding H T, Hegde P et al, Phys. Rev. D, 95:054504 (2017)
[8]	Y. Aoki, G. Endrdi, Z. Fodor, S. D. Katz, and K. K. Szab, Nature, 443:675 (2006)
[9]	M. A. Stephanov, K. Rajagopal, and E. V. Shuryak, Phys. Rev. D, 60:114028 (1999)
[10]	V. Koch, arXiv:0810.2520
[11]	M. Cheng et al, Phys. Rev. D, 79:074505 (2009)
[12]	L. Adamczyk et al (STAR Collaboration), Phys. Rev. Lett., 112:032302 (2014)
[13]	L. Adamczyk et al (STAR Collaboration), Phys. Rev. Lett., 113:092301 (2014)
[14]	F. Karsch, Cent. Eur. J. Phys., 10:1234 (2012)
[15]	A. Bazavov et al, Phys. Rev. Lett., 109:192302 (2012)
[16]	R. Bellwied, S. Borsanyi, Z. Fodor, S. D. Katz, A. Pasztor, C. Ratti, and K. K. Szabo, Phys. Rev. D, 92:114505 (2015)
[17]	S. Borsanyi, Z. Fodor, S. D. Katz, S. Krieg, C. Ratti, and K. K. Szabo, Phys. Rev. Lett., 111:062005 (2013); Phys. Rev. Lett., 113:052301 (2014)
[18]	M. Asakawa, S. Ejiri, and M. Kitazawa, Phys. Rev. Lett., 103:262301 (2009)
[19]	W. J. Fu and Y. L. Wu, Phys. Rev. D, 82:074013 (2010)
[20]	M. A. Stephanov, Phys. Rev. Lett., 107:052301 (2011)
[21]	B. Friman, F. Karsch, K. Redlich, and V. Skokov, Eur. Phys. J. C, 71:1694 (2011)
[22]	J. W. Chen, J. Deng, H. Kohyama, and L. Labun, Phys. Rev. D, 93:034037 (2016); Phys. Rev. D, 95:014038 (2017)
[23]	X. Pan, L. Z. Chen, X. S. Chen, and Y. F. Wu, Nucl. Phys. A, 913:206 (2013)
[24]	A. Patel, Nucl. Phys. B, 243:411 (1984); A. Patel, Phys. Lett. B, 139:394 (1984)
[25]	H. W. J. Blte and R. H. Swendsen, Phys. Rev. Lett., 43:799 (1979)
[26]	W. Janke and R. Villanova, Nucl. Phys. B, 489:679 (1997)
[27]	F. Karsch and S. Stickan, Phys. Lett. B, 488:319 (2000)
[28]	X. Pan, M. M. Xu, and Y. F. Wu, J. Phys. G:Nucl. Part. Phys., 42:015104 (2015)
[29]	F. Y. Wu, Rev. Mod. Phys., 54:235 (1982)
[30]	U. Wolff, Phys. Rev. Lett., 62:361 (1989)
[31]	V. Privman and M. E. Fisher, Phys. Rev. B, 30:322 (1984)
[32]	X. S. Chen, V. Dohm, and A. L. Talapov, Physica A:Statistical Mechanics and its Applications, 232:375 (1996)
[33]	V. Privman, Finite Size Scaling and Numerical Simulation of Statistical Systems (Singapore:World Scientific) (1990)
[34]	H. W. J. Blte, E. Luijten, and J. R. Heringa, J. Phys. A:Math. Gen., 28:6289 (1995)

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Xue Pan, Yanhua Zhang, Lizhu Chen, Mingmei Xu and Yuanfang Wu. Finite-size behaviour of generalized susceptibilities in the whole phase plane of the Potts model[J]. Chinese Physics C, 2018, 42(2): 023110. doi: 10.1088/1674-1137/42/2/023110

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Received: 2017-09-29
Revised: 2017-12-03

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Supported by Fund Project of National Natural Science Foundation of China (11647093, 11405088, 11521064), Fund Project of Sichuan Provincial Department of Education (16ZB0339), Fund Project of Chengdu Technological University (2016RC004) and the Major State Basic Research Development Program of China (2014CB845402)

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沈阳化工大学材料科学与工程学院沈阳 110142

Finite-size behaviour of generalized susceptibilities in the whole phase plane of the Potts model

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Finite-size behaviour of generalized susceptibilities in the whole phase plane of the Potts model

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