A classification of string solutions of the Bethe equations for the $XXZ$ model of arbitrary spin

The structure of string solutions for the $XXZ$ Heisenbers model of arbitrary spin is studied. Special spin values are found for which there are restrictions on the positions of centers of certain string solutions. For a class of spin values depending on the asnisothropy parameter such restrictions do not occur. A conjecture on the full classification of string states over the ferromagnetic vacuum is formulated. Bibl. – 14.