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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 |
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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.
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Received: 15 April 2025
Revised: 02 May 2025
Accepted manuscript online: 07 May 2025
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PACS:
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05.20.Gg
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(Classical ensemble theory)
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05.10.-a
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(Computational methods in statistical physics and nonlinear dynamics)
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05.50.+q
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(Lattice theory and statistics)
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05.70.-a
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(Thermodynamics)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11974420). |
Corresponding Authors:
Ning-Hua Tong
E-mail: nhtong@ruc.edu.cn
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Cite this article:
Hu-Wei Jia(贾虎伟) and Ning-Hua Tong(同宁华) Thermodynamics of classical one-dimensional generalized nonlinear Klein-Gordon lattice model 2025 Chin. Phys. B 34 080501
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