The Integrability Condition of Three-Dimensional Exactly Solvable 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(2) : 123-130

The Integrability Condition of Three-Dimensional Exactly Solvable Model-Baxter-Bazhanov Model in Statistical Mechanics

Hu Zhanning ^, ,
Hou Boyu

Institute of Modern Physics.Northwest University,Xi'an 710069

Abstract
HTML
Reference
Related

PDF

Abstract：
From the chiral Potts model the"inversion"and"star-square"relations of the Baxter-Bazhanov model are obtained.This means that 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 parametrized in terms of the Zamolodchikov angle variables.It is point out that the star-triangle relation of the three-dimensional model can be gotten by using the method given in this paper,which includes the result of Baxter and Bazhanov's.

References

[1]

R.J.Baxter,Exactly solved models in statistical mechanics（Academic Press,London,1982）.[2]V.V.Bazhanov,R.J.Baxter,J.Stat.Phys.,69（1992）453.[3]A.B.Zamolodchikov.Commun.Math.Phys.,79（1981）489. [4]R.M.Kashaev,V.V.Mangazeev,Yu.G.Stroganov,Int.J.Mod.Phys.,A8（1993）1399.[5]R.J.Baxter,J.H.H.Perk,Phys.Lett.,A128（1988）138.V.B.Matveev,A.O.Smirnov,Some Comments on the Solvable Chiral Potts Model,pre-print.[6]V.V.Bazhanov,R.J.Baxter,J.Stat.Phys.,71（1993）839.[7]R.M.Kashaev,V.V.Mangazeev,Yu.G.Stroganov,Int.J.Mod.Phys.,A8（1993）587.

[1]	San-Min Ke , Wen-Li Yang , Ke-Xia Jang , Chun Wang , Xue-Min Shuai , Zhan-Yun Wang , Gang Shi . Yang-Baxter deformations of supercoset sigma models with Z_4m grading. Chinese Physics C, 2017, 41(11): 113101. doi: 10.1088/1674-1137/41/11/113101
[2]	CAO Li-Ke , KE San-Min , YANG Tao , YUE Rui-Hong . Exact Solution of a New Class of Hubbard-Type Models with Open Boundary Conditions. Chinese Physics C, 2007, 31(1): 30-33.
[3]	LU He-Lin , WANG Shun-Jin . High-Harmonic Generation by Intense Laser Fields Interacting with Atoms in Three Dimensional and Two-Level Hydrogen Atom Model. Chinese Physics C, 2006, 30(11): 1137-1140.
[4]	ZHOU Yi , LI Cheng , AN Shao-Hui , XU Zi-Zong . Three Dimension Distribution of Electric Field in GEM Gas Detectors. Chinese Physics C, 2004, 28(3): 299-303.
[5]	ZHAO Xiu-Mei , CAO Li-Ke , YANG Tao , YUE Rui-Hong . Integrability of a Quantum Derivative Nonlinear Schrodinger Model for Spin-1/2 Particle. Chinese Physics C, 2004, 28(9): 936-940.
[6]	YAN Jun , TAO Bi-You . A Electric Sine-Gordon Soliton Solution in Two-Dimensional Dilaton Gravity Model. Chinese Physics C, 2003, 27(9): 767-769.
[7]	YANG ZhanYing , ZHAO Liu , ZHEN Yi . Exact Solution of Super Liouville Model. Chinese Physics C, 2000, 24(2): 91-97.
[8]	Ma Tao , Ni Zhixiang . Non-Harmonic Oscillator and New Conditionally Exactly Solvable Potentials. Chinese Physics C, 1999, 23(7): 650-654.
[9]	Zhang Jun , Guo Hanying , Yan Hong . Knitting Ansatz and Solutions to Yang-Baxter Equation. Chinese Physics C, 1997, 21(8): 714-719.
[10]	Yue Ruihong , Liang Hong . Integrability and Boundary Conditions of Supersymmetric Systems. Chinese Physics C, 1996, 20(6): 514-521.
[11]	Hu Zhanning , Hou Boyu . Integrability Conditions of the Three-dimensional Exactly Solved Model-Baxter-Bazhanov Model in Statistical Mechanics. Chinese Physics C, 1995, 19(S2): 143-150.
[12]	Hu Zhanning . Three-Dimensional Exactly Solvable Model With Cubic Lattice. Chinese Physics C, 1994, 18(9): 813-820.
[13]	ZHAO Liu . From Integrability to Conformal Symmetry: Bosonic Superconformal Toda Theories. Chinese Physics C, 1993, 17(5): 431-443.
[14]	YAN Jun , HU Shi-Ke . A Solvable Model in Two-Dimensional Quantum Gravity. Chinese Physics C, 1991, 15(7): 598-605.
[15]	ZHENG Bo . A(1+1)-DIMENSIONAL LATTICE U(1) GAUGE MODEL AND THE FERMION SPECIES DOUBLING. Chinese Physics C, 1990, 14(4): 375-379.
[16]	ZHENG Bo , GUO Shuo-Hong . A SOLVABLE 1+1-DIMENSIONAL U(1) GAUGE THEORY. Chinese Physics C, 1990, 14(2): 152-155.
[17]	SONG Zhong-Heng , WANG Xiao-Min . THREE-DIMENSIONAL DYNAMIC CALCULATION OF CHARGE DISC WITH VARIABLE RADIUS OF ELECTRON LINAC. Chinese Physics C, 1990, 14(1): 16-23.
[18]	CHEN Tian-Lun , HUANG Wu-Qun , SHEN Qin-Wan . A MONTE CARLO RENORMALIZATION GROUP STUDY OF ISING MODEL ON THREE-DIMENSIONAL RANDOM TRIANGLE LATTICE. Chinese Physics C, 1988, 12(4): 573-576.
[19]	CAI Xu , WU Yuan-Fang , LIU Lian-Shou . ENERGY DEPENDENCE OF MULTIPLICITY MOMENTS AND THREE FIRE BALL MODEL. Chinese Physics C, 1987, 11(4): 554-557.
[20]	XU Yong-Xing , MA Ying-Jie . CALCULATION OF THE 3-DIMENSIONAL MAGNETIC FIELD BY USE OF THE MODIFIED SCALAR POTENTIAL. Chinese Physics C, 1984, 8(3): 370-373.

Access

Get Citation

Hu Zhanning and Hou Boyu. The Integrability Condition of Three-Dimensional Exactly Solvable Model-Baxter-Bazhanov Model in Statistical Mechanics[J]. Chinese Physics C, 1995, 19(2): 123-130.

Hu Zhanning and Hou Boyu. The Integrability Condition of Three-Dimensional Exactly Solvable Model-Baxter-Bazhanov Model in Statistical Mechanics[J]. Chinese Physics C, 1995, 19(2): 123-130. shu

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 1900-01-01
Revised: 1900-01-01

Article Metric

Article Views(3001)
PDF Downloads(541)
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, [email protected]

1.
沈阳化工大学材料科学与工程学院沈阳 110142

The Integrability Condition of Three-Dimensional Exactly Solvable Model-Baxter-Bazhanov Model in Statistical Mechanics

Hu Zhanning ^,
Hou Boyu

Corresponding author: Hu Zhanning,

Institute of Modern Physics.Northwest University,Xi'an 710069

Received Date: 1900-01-01
Accepted Date: 1900-01-01
Available Online: 1995-02-05

Abstract: From the chiral Potts model the"inversion"and"star-square"relations of the Baxter-Bazhanov model are obtained.This means that 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 parametrized in terms of the Zamolodchikov angle variables.It is point out that the star-triangle relation of the three-dimensional model can be gotten by using the method given in this paper,which includes the result of Baxter and Bazhanov's.