Integrability Conditions of the Three-dimensional Exactly Solved Model-Baxter-Bazhanov Model in Statistical Mechanics

Hu Zhanning; Hou Boyu

近期发现有不法分子冒充我刊与作者联系，借此进行欺诈等不法行为，请广大作者加以鉴别，如遇诈骗行为，请第一时间与我刊编辑部联系确认（《中国物理C》（英文）编辑部电话：010-88235947,010-88236950），并作报警处理。

本刊再次郑重声明：

（1）本刊官方网址为cpc.ihep.ac.cn和https://iopscience.iop.org/journal/1674-1137

（2）本刊采编系统作者中心是投稿的唯一路径，该系统为ScholarOne远程稿件采编系统，仅在本刊投稿网网址（https://mc03.manuscriptcentral.com/cpc）设有登录入口。本刊不接受其他方式的投稿，如打印稿投稿、E-mail信箱投稿等，若以此种方式接收投稿均为假冒。

（3）所有投稿均需经过严格的同行评议、编辑加工后方可发表，本刊不存在所谓的“编辑部内部征稿”。如果有人以“编辑部内部人员”名义帮助作者发稿，并收取发表费用，均为假冒。

《中国物理C》（英文）编辑部

2024年10月30日

Chinese Physics C> 1995, Vol. 19> Issue(S2) : 143-150

Integrability Conditions of the Three-dimensional Exactly Solved Model-Baxter-Bazhanov Model in Statistical Mechanics

Hu Zhanning ,
Hou Boyu

Institute of Modem Physics, Northwest University, Xian, China

Abstract
HTML
Reference
Related

PDF

Abstract：
From the chiral Potts model the "inversion" and "star-square" relations of the Baxter-Bazhanov model are obtained. The tetrahedron equation, which is a commutativity condition for the three-dimensional cubic lattice, is a consequence of the star-triangle relation of the chiral Potts model. The additional constraints in tetrahedron equation hold naturally when the Boltzmann weights are parameterized in terms of the Zamolodchikov angle variables. It is pointed out that the star-triangle relation of the three-dimensional model, which includes the result of Baxter-Bazhanov's, can be obtained by using the method given in this paper.
- chiral Potts model ,
- Baxter-Bazhanov model ,
- “Star-Square” relation ,
- Tetrahedron equation ,
- Star-Triangle relation

[1]	Xue Pan , Yanhua Zhang , Lizhu Chen , Mingmei Xu , Yuanfang Wu . Finite-size behaviour of generalized susceptibilities in the whole phase plane of the Potts model. Chinese Physics C, 2018, 42(2): 023110. doi: 10.1088/1674-1137/42/2/023110
[2]	Yubing Dong , Fei Huang , Pengnian Shen , Zongye Zhang . On the decays of d^* in a constituent chiral quark model. Chinese Physics C, 2017, 41(10): 101001. doi: 10.1088/1674-1137/41/10/101001
[3]	ZHAO Xian-Feng , JIA Huan-Yu . Transition density of the large mass hyperon star. Chinese Physics C, 2014, 38(1): 015101. doi: 10.1088/1674-1137/38/1/015101
[4]	CHEN Shao-Na , PING Jia-Lun . Radial excitation states of η and η' in the chiral quark model. Chinese Physics C, 2012, 36(8): 681-690. doi: 10.1088/1674-1137/36/8/001
[5]	LI Ming-Tao , DONG Yu-Bing , ZHANG Zong-Ye . A study of meson-meson potential in the chiral quark model. Chinese Physics C, 2011, 35(7): 622-628. doi: 10.1088/1674-1137/35/7/005
[6]	ZHAO Xian-Feng , ZHANG Hua , JIA Huan-Yu . On the moment of inertia of a proto neutron star. Chinese Physics C, 2010, 34(10): 1587-1592. doi: 10.1088/1674-1137/34/10/007
[7]	ZHONG Xian-Hui , ZHAO Qiang . K^－p scattering and hyperon excitations in a chiral quark model. Chinese Physics C, 2010, 34(9): 1428-1432. doi: 10.1088/1674-1137/34/9/062
[8]	LI Ang , PENG Guang-Xiong , Lombardo U . Deconfinement phase transition in neutron star matter. Chinese Physics C, 2009, 33(S1): 61-63. doi: 10.1088/1674-1137/33/S1/020
[9]	HE Jun . Study of nucleon resonances in a chiral quark model via η productions. Chinese Physics C, 2009, 33(12): 1389-1392. doi: 10.1088/1674-1137/33/12/062
[10]	ZHONG Xian-Hui , ZHAO Qiang . Λ resonances studied in K^－p→Σ⁰π⁰ in a chiral quark model. Chinese Physics C, 2009, 33(12): 1373-1376. doi: 10.1088/1674-1137/33/12/058
[11]	SUN Bao-Yuan , MENG Jie . Neutron star equation of state in density dependent relativistic Hartree-Fock theory. Chinese Physics C, 2009, 33(S1): 73-75. doi: 10.1088/1674-1137/33/S1/024
[12]	Hu Zhanning , Hou Boyu . The Integrability Condition of Three-Dimensional Exactly Solvable Model-Baxter-Bazhanov Model in Statistical Mechanics. Chinese Physics C, 1995, 19(2): 123-130.
[13]	Deng Shenghua , Li Jiarong . Equation of State in the F-L Model and a Physical Picture of Deconfinement Transition. Chinese Physics C, 1994, 18(Z1): 49-54.
[14]	Hu Zhanning . Three-Dimensional Exactly Solvable Model with Cubic Lattice. Chinese Physics C, 1994, 18(S3): 291-300.
[15]	Wang Enke , Li Jiarong . The Equation of State and Phase Structure in A Model with Dynamical Spontaneous Symmetry Breaking at Finite Temperature and Density. Chinese Physics C, 1992, 16(S2): 193-200.
[16]	SONG Yong-Shen , CUI Jian-Ying , YANG Ji-Min , LU Gong-Ru , LIU Wen-Sheng . The Phase Transition in Z(N) Potts Spin Model: An Analytical Analysis. Chinese Physics C, 1992, 16(7): 588-595.
[17]	Shen Kun , Qiu Zhongping . Chiral Symmetry, Ward-Takahashi Identities and Mass spectra in (2 + 1) Dimensional Chiral Gross-Neveu Model. Chinese Physics C, 1991, 15(S4): 401-410.
[18]	Xu Xiaoming , Qiu Xijun . A Chiral Quark-Soliton Model Theory for Nuclear Force. Chinese Physics C, 1990, 14(S4): 381-389.
[19]	Chen Tianlun . β Function for the 0(3) Sigma Model on 2-Dimensional Random Triangle Lattice. Chinese Physics C, 1989, 13(S4): 393-398.
[20]	Chen Tianlun , Huang Wuqun , Jin Ke , Suo Cunchuan . β Function tor SU(2)×SU(2) Chiral Model on 2-Dimensional Random Triangle Lattice. Chinese Physics C, 1989, 13(S1): 43-48.

Access

Get Citation

Hu Zhanning and Hou Boyu. Integrability Conditions of the Three-dimensional Exactly Solved Model-Baxter-Bazhanov Model in Statistical Mechanics[J]. Chinese Physics C, 1995, 19(S2): 143-150.

Hu Zhanning and Hou Boyu. Integrability Conditions of the Three-dimensional Exactly Solved Model-Baxter-Bazhanov Model in Statistical Mechanics[J]. Chinese Physics C, 1995, 19(S2): 143-150. shu

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 1993-12-21

Article Metric

Article Views(680)
PDF Downloads(3)
Cited by(0)

Policy on re-use

To reuse of subscription content published by CPC, the users need to request permission from CPC, unless the content was published under an Open Access license which automatically permits that type of reuse.

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

Integrability Conditions of the Three-dimensional Exactly Solved Model-Baxter-Bazhanov Model in Statistical Mechanics

Hu Zhanning
Hou Boyu

Institute of Modem Physics, Northwest University, Xian, China

Received Date: 1993-12-21

Abstract: From the chiral Potts model the "inversion" and "star-square" relations of the Baxter-Bazhanov model are obtained. The tetrahedron equation, which is a commutativity condition for the three-dimensional cubic lattice, is a consequence of the star-triangle relation of the chiral Potts model. The additional constraints in tetrahedron equation hold naturally when the Boltzmann weights are parameterized in terms of the Zamolodchikov angle variables. It is pointed out that the star-triangle relation of the three-dimensional model, which includes the result of Baxter-Bazhanov's, can be obtained by using the method given in this paper.