Abstract
We show that aZ(N 2)-spin model proposed by A. B. Zamolodchikov and M. I. Monastyrskii can be conveniently described by two interactingN-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 staggeredZ(N)-symmetric vertex model, which turns out to be a generalization of theN-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 N2-state andN-state Potts models by staggered Schultz-Perk vertex models, as compared to the usual representation by staggered six-vertex models.
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Truong, T.T. Structural properties of aZ(N 2)-spin model and its equivalentZ(N)-vertex model. J Stat Phys 42, 349–379 (1986). https://doi.org/10.1007/BF01127716
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DOI: https://doi.org/10.1007/BF01127716