3-DIMENSIONAL VERTEX MODEL IN STATISTICAL-MECHANICS FROM BAXTER-BAZHANOV MODEL

We find that the Boltzmann weight of the three-dimensional Baxter-Bazh anov model is dependent on four spin variables which are the linear co mbinations of the spins on the corner sites of the cube, and the Wu-Ka danoff-Wegner duality between the cube- and vertex-type tetrahedron eq uations is obtained explicitly for the Baxter-Bazhanov model. Then a t hree-dimensional vertex model is obtained by considering the symmetry property of the weight function, which corresponds to the three-dimens ional Baxter-Bazhanov model. The vertex-type weight function is parame trized as the dihedral angles between the rapidity planes connected wi th the cube. We write down the symmetry relations of the weight functi ons under the actions of the symmetry group G of the cube. The six ang les with a constraint condition appearing in the tetrahedron equation can be regarded as the six spectra connected with the six spaces in wh ich the vertex-type tetrahedron equation is defined.