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

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.