Analysis of the Bethe ansatz equations of the XXZ model

We analyse the Bethe ansatz equations of the XXZ model in the antiferromagnetic region, without assuming a priori the existence of strings. Excited states are described by a finite number of parameters. These parameters satisfy a closed system of equations, which we obtain by eliminating the parameters of the vacuum from the original Bethe ansatz equations. Strings are only particular solutions of these equations.