Classification and completeness of Bethe states and excitation spectrum for the spin 4 Fateev-Zamolodchikov model

The classification and completeness of Bethe states is undertaken for the spin 4 Fateev-Zamolodchikov model. This special case is of particular interest as the energy can be derived in a simple closed form even for lattices of arbitrary finite size. The excitation spectrum over the ferromagnetic ground state is also derived.