Abstract
In this paper we study both analytical and combinatorial properties of solutions of the eigenproblem for the Heisenberg s-1/2 model for two deviations. Our analysis uses Chebyshev polynomials, inverse Bethe Ansatz, winding numbers and rigged string configurations. We show some combinatorial aspects of strings in a geometric way. We discuss some exceptions from the connection between the combinatorial nature of an eigenstate and the analytical type of a solution of the eigenproblem. In particular, as an illustration of the aforementioned exceptions, we analyze the singularities of Bethe parameters for bound states at the border of the Brillouin zone.
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