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

Hu Zhanning; Hou Boyu

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《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

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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

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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

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Received: 1993-12-21

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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.