STAR TRIANGLE RELATION FOR A 3-DIMENSIONAL MODEL

The solvable sl(n)-chiral Potts model can be interpreted as a three-di mensional lattice model with local interactions. To within a minor mod ification of the boundary conditions it is an Ising-type model on the body-centered cubic lattice with two- and three-spin interactions. The corresponding local Boltzmann weights obey a number of simple relatio ns, including a restricted star-triangle relation, which is a modified version of the well-known star-triangle relation appearing in two-dim ensional models. We show that these relations lead to remarkable symme try properties of the Boltzmann weight function of an elementary cube of the lattice, related to the spatial symmetry group of the cubic lat tice. These symmetry properties allow one to prove the commutativity o f the row-to-row transfer matrices, bypassing the tetrahedron relation . The partition function per site for the infinite lattice is calculat ed exactly.