SPATIAL SYMMETRY, LOCAL INTEGRABILITY AND TETRAHEDRON EQUATIONS IN THE BAXTER-BAZHANOV MODEL

Abstract

We show that the Baxter-Bazhanov model is invariant under the action of the cube’s symmetry group. The three-dimensional star-star relations, proposed by Baxter and Bazhanov as local integrability conditions, correspond to a particular transformation from this group. Invariant Boltzmann weights, parametrized in terms of the Zamolodchikov angle variables, apparently satisfy the tetrahedron equations.