Thermodynamics of classical one-dimensional generalized nonlinear Klein-Gordon lattice model

doi:10.1088/1674-1056/add50f

中国物理B ›› 2025, Vol. 34 ›› Issue (8): 80501-080501.doi: 10.1088/1674-1056/add50f

Thermodynamics of classical one-dimensional generalized nonlinear Klein-Gordon lattice model

Hu-Wei Jia(贾虎伟)^1,2 and Ning-Hua Tong(同宁华)^1,2,†

1 School of Physics, Renmin University of China, Beijing 100872, China;
2 Key Laboratory of Quantum State Construction and Manipulation (Ministry of Education), Renmin University of China, Beijing 100872, China

收稿日期:2025-04-15 修回日期:2025-05-02 接受日期:2025-05-07 出版日期:2025-07-17 发布日期:2025-08-08
通讯作者: Ning-Hua Tong E-mail:nhtong@ruc.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11974420).

Thermodynamics of classical one-dimensional generalized nonlinear Klein-Gordon lattice model

Hu-Wei Jia(贾虎伟)^1,2 and Ning-Hua Tong(同宁华)^1,2,†

1 School of Physics, Renmin University of China, Beijing 100872, China;
2 Key Laboratory of Quantum State Construction and Manipulation (Ministry of Education), Renmin University of China, Beijing 100872, China

Received:2025-04-15 Revised:2025-05-02 Accepted:2025-05-07 Online:2025-07-17 Published:2025-08-08
Contact: Ning-Hua Tong E-mail:nhtong@ruc.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11974420).

摘要/Abstract

摘要： We study the thermodynamic properties of the classical one-dimensional generalized nonlinear Klein-Gordon lattice model ($n \ge 2$) by using the cluster variation method with linear response theory. The results of this method are exact in the thermodynamic limit. We present the single-site reduced density $\rho^{(1)}(z)$, averages such as $\langle z^2 \rangle$, $\langle |z^n|\rangle$, and $\langle (z_1-z_2)^2\rangle$, the specific heat $C_{\rm v}$, and the static correlation functions. We analyze the scaling behavior of these quantities and obtain the exact scaling powers at the low and high temperatures. Using these results, we gauge the accuracy of the projective truncation approximation for the $\phi^{4}$ lattice model.

关键词: cluster variation method, linear response theory, one-dimensional generalized nonlinear Klein-Gordon lattice model

Abstract: We study the thermodynamic properties of the classical one-dimensional generalized nonlinear Klein-Gordon lattice model ($n \ge 2$) by using the cluster variation method with linear response theory. The results of this method are exact in the thermodynamic limit. We present the single-site reduced density $\rho^{(1)}(z)$, averages such as $\langle z^2 \rangle$, $\langle |z^n|\rangle$, and $\langle (z_1-z_2)^2\rangle$, the specific heat $C_{\rm v}$, and the static correlation functions. We analyze the scaling behavior of these quantities and obtain the exact scaling powers at the low and high temperatures. Using these results, we gauge the accuracy of the projective truncation approximation for the $\phi^{4}$ lattice model.

Key words: cluster variation method, linear response theory, one-dimensional generalized nonlinear Klein-Gordon lattice model

中图分类号: (Classical ensemble theory)

05.20.Gg

05.10.-a (Computational methods in statistical physics and nonlinear dynamics) 05.50.+q (Lattice theory and statistics) 05.70.-a (Thermodynamics)

Hu-Wei Jia(贾虎伟) and Ning-Hua Tong(同宁华). Thermodynamics of classical one-dimensional generalized nonlinear Klein-Gordon lattice model[J]. 中国物理B, 2025, 34(8): 80501-080501.

Hu-Wei Jia(贾虎伟) and Ning-Hua Tong(同宁华). Thermodynamics of classical one-dimensional generalized nonlinear Klein-Gordon lattice model[J]. Chin. Phys. B, 2025, 34(8): 80501-080501.

参考文献

[1] Lepri S 2016 Thermal Transport in Low Dimensions: from Statistical Physics to Nanoscale Heat Transfer (Cham: Springer)
[2] Niss K and Hecksher T 2018 J. Chem. Phys. 149 230901
[3] Arceri F, Landes F P, Berthier L and Biroli G 2020 arXiv:2006.09725[cond-mat.stat-mech]
[4] Debenedetti P G and Stillinger F H 2001 Nature 410 259
[5] Ise N 1986 Angew. Chem. Int. Ed. Engl. 25 323
[6] Gebbie M A, Valtiner M, Banquy X, Fox E T, Henderson W A and Israelachvili J N 2013 Proc. Natl. Acad. Sci. USA 110 9674
[7] Bloomfield V A 1996 Curr. Opin. Struct. Biol. 6 334
[8] Ubbink J and Odijk T 1995 Biophys. J. 68 54
[9] Metropolis N and Ulam S 1949 J. Amer. Statist. Assoc. 44 335
[10] Fermi E, Pasta P, Ulam S and TsingouM1955 Studies of the Nonlinear Problems (New Mexico: Los Alamos Scientific Laboratory)
[11] Alder B J and Wainwright T E 1959 J. Chem. Phys. 31 459
[12] Netz R R and Orland H 2003 Eur. Phys. J. E 11 301
[13] Liu J, Li B and Wu C 2016 Europhys. Lett. 114 40002
[14] Liu J, Liu S, Li N, Li B and Wu C 2015 Phys. Rev. E 91 042910
[15] Wu J and Cao J 2005 Phys. Rev. Lett. 95 078301
[16] Szamel G 2013 Prog. Theor. Exp. Phys. 2013 012J01
[17] Xu Y, Wang J S, Duan W, Gu B L and Li B 2008 Phys. Rev. B 78 224303
[18] Ma K H, Guo Y J,Wang L and Tong N H 2022 Phys. Rev. E 106 014110
[19] Jia HW, LiuWJ,Wu Y H, Ma K H,Wang L and Tong N H 2025 Phys. Rev. B 111 045153
[20] Li N and Li B 2013 Phys. Rev. E 87 042125
[21] Parisi G 1997 Europhys. Lett. 40 357
[22] Boyanovsky D, Destri C and de Vega H J 2004 Phys. Rev. D 69 045003
[23] Aoki K and Kusnezov D 2000 Phys. Lett. A 265 250
[24] Kikuchi R 1951 Phys. Rev. 81 988
[25] Kubo R 1957 J. Phys. Soc. Jpn. 12 570
[26] Pelizzola A 2000 Nucl. Phys. B 83–84 706
[27] Pelizzola A 2005 J. Stat. Mech. 2005 P11010
[28] Pelizzola A 2005 J. Phys. A: Math. Gen. 38 R309
[29] Peierls R E 1938 Phys. Rev. 54 918
[30] For a review, see Kuzemsky A L 2015 Int. J. Mod. Phys. B 29 1530010
[31] Feynman R P 1972 Statistical Mechanics (New York: W. A. Benjamin Inc.)
[32] Morita T 1957 J. Phys. Soc. Jpn. 12 753
[33] Morita T 1957 J. Phys. Soc. Jpn. 12 1060
[34] An G 1988 J. Stat. Phys. 52 727
[35] Morita T 1990 J. Stat. Phys. 59 819
[36] Brascamp H J 1971 Commun. Math. Phys. 21 56
[37] Percus J K 1977 J. Stat. Phys. 16 299
[38] Kikuchi R and Beldjenna A 1992 Physica A 182 617
[39] Kikuchi R 1998 J. Phase Equilib. 19 412
[40] Kikuchi R 1999 J. Stat. Phys. 95 1323
[41] Ren Y Z, Tong N H and Xie X C 2014 J. Phys.: Condens. Matter 26 115601
[42] Yamamoto D 2009 Phys. Rev. B 79 144427
[43] Kikuchi R 1951 J. Chem. Phys. 19 1230
[44] Ng W M and Barry J H 1978 Phys. Rev. B 17 3675
[45] Cirillo E N M, Gonnella G, Troccoli M and Maritan A 1999 J. Stat. Phys. 94 67
[46] Guerrero A I, Stariolo D A and Almarza N G 2015 Phys. Rev. E 91 052123
[47] Guerrero A I, Stariolo D A 2017 Physica A 466 596
[48] Kikuchi R 1974 J. Chem. Phys. 60 1071
[49] McCormack R, Asta M, de Fontaine D, Garbulsky G and Ceder G 1993 Phys. Rev. B 48 6767
[50] Sanchez J M, Ducastelle F and Gratias D 1984 Physica A 128 334
[51] Morita T and Tanaka T 1966 Phys. Rev. 145 288
[52] Tanaka T and Libelo L F 1975 Phys. Rev. B 12 1790
[53] Halow J, Tanaka T and Morita T 1968 Phys. Rev. 175 680
[54] Morita T 1994 Prog. Theor. Phys. 92 1081
[55] Tanaka T, Hirose K and Kurati K 1994 Prog. Theor. Phys. Suppl. No. 115 41
[56] Finel A 1994 Suppl. Prog. Theor. Phys. 115 59
[57] Mohri T 2013 JOM 65 1510
[58] Tanaka K 2003 IEICE Trans. on Information and Systems E86-D 1228
[59] Tanaka K 2005 International Conference on Computational Intelligence for Modelling, Control and Automation and International Conference on Intelligent Agents, Web Technologies and Internet Commerce (CIMCA-IAWTIC’06) November 28–30, 2005, Vienna, Austria, pp. 669–675
[60] Das A 2008 Lectures on Quantum Field Theory (Hackensack, USA: World Scientific)
[61] Dmitriev S V, Kevrekidis P G and Yoshikawa N 2006 J. Phys. A: Math. Gen. 39 7217
[62] Xu L and Wang L 2016 Phys. Rev. E 94 030101
[63] Liu Y and He D 2021 Chin. Phys. Lett. 38 044401
[64] Yang L, Li N and Li B 2014 Phys. Rev. E 90 062122
[65] Aoki K and Kusnezov D 2001 Phys. Rev. Lett. 86 4029
[66] Gillan M J 1984 J. Phys. C: Solid State Phys. 17 L237
[67] Casati G, Ford J, Vavaldi F and Visscher W M 1984 Phys. Rev. Lett. 52 1861
[68] Onodera Y 1970 Prog. Theor. Phys. 44 1477
[69] Toda M 1967 J. Phys. Soc. Jpn. 22 431
[70] Toda M 1967 J. Phys. Soc. Jpn. 23 501
[71] Mareschal M and Amellal A 1988 Phys. Rev. A 37 2189
[72] Morán-López J L and Sanchez J M 1996 Theory and Applications of the Cluster Variational and Path Probability Methods (New York and London: Plenum Press)

Thermodynamics of classical one-dimensional generalized nonlinear Klein-Gordon lattice model

Thermodynamics of classical one-dimensional generalized nonlinear Klein-Gordon lattice model

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