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Journal of Mathematical Physics

Factorized S matrices and generalized Baxter models

Anton Bovier

Published Mar 1, 1983• 19 citations
Publisher

Abstract

We prove that solutions of the factorization equations for S matrices with Zn symmetry can be given in terms of theta functions. We present a class of vertex models based on A-symmetric S matrices (A being an abelian group) as natural generalizations of the Baxter model. The mapping of these models into spin systems is described.
DOI
10.1063/1.525709

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In this paper we review the theory of the Yang–Baxter equation related to the 6-vertex model and its higher spin generalizations. We employ a 3D approach to the problem. Starting with the 3D R-matrix, we consider a two-layer projection of the corresponding 3D lattice model. As a result, we obtain a new expression for the higher spin R-matrix associated with the affine quantum algebra Uq(sl(2)ˆ). In the simplest case of the spin s=1/2 this R-matrix naturally reduces to the R-matrix of the 6-vertex model. Taking a special limit in our construction we also obtain new formulas for the Q-operators acting in the representation space of arbitrary (half-)integer spin. Remarkably, this construction can be naturally extended to any complex values of spin s. We also give all functional equations satisfied by the transfer-matrices and Q-operators.