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arXiv:hep-th/9410049 · Modern Physics Letters A

NEW SOLUTION OF VERTEX TYPE TETRAHEDRON EQUATIONS

Vladimir V. Mangazeev, С. М. Сергеев, Yu. G. Stroganov

Published Feb 10, 1995• 8 citations
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Abstract

In this letter we formulate a new N-state spin integrable model on a three-dimensional lattice with spins interacting round each elementary cube of the lattice. This model can also be reformulated as a vertex type model. Weight functions of the model satisfy tetrahedron equations.
DOI
10.1142/s0217732395000314

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In this paper we present a new series of three-dimensional integrable lattice models with N colors. The case N=2 generalizes the elliptic model of Ref. 8. The weight functions of the models satisfy modified tetrahedron equations with N states and give a commuting family of two-layer transfer matrices. The dependence on the spectral parameters corresponds to the static limit of the modified tetrahedron equations, and weights are parametrized in terms of elliptic functions. The models contain two free parameters: elliptic modulus and additional parameter η. Also, we briefly discuss symmetry properties of weight functions of the models.
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