Journal of Statistical Physics, Vo!. 42, Nos. 3/4, 1986, p. 349-379.
We show that a Z(N^2)-spin model proposed by A. B. Zamolodchikov and M. I. Monastyrskii can be conveniently described by two interacting N-state Potts models. We study its properties, especially by using a dual invariant quantity of the model. A partial duality performed on one set of Potts spins yields a staggered Z(N)-symmetric vertex model, which turns out to be a generalization of the N-state "nonintersecting string model" of C. L. Schultz and J. H. H. Perk. We describe its properties and elaborate on its (pseudo) "weak-graph symmetry." As by-products we find alternative representations of the N^2-state and N-state Potts models by staggered Schultz-Perk vertex models, as compared to the usual representation by staggered six-vertex models.