Abstract:The general concept of integrability in the framework of the Algebraic Bethe Ansatz is discussed and combined non-homogeneous local integrability equations are proposed for general D dimensional vertex statistical models. For 2D the efficiency of the step by step consideration of the Ansatz avoiding the direct analysis of Yang-Baxter equations is demonstrated. Also 3D three-state R-matrices with certain 20-vertex structure are discussed and there are constructed some simple 3D vertex solutions. The simplified … Show more
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