BETHE-ANSATZ TYPE EQUATIONS FOR THE FATEEV-ZAMOLODCHIKOV SPIN MODEL

The eigenvalues of the Fateev-Zamolodchikov Z(N) invariant model transfer matrix are found for N odd. Their zeros in the complex plane of the rapidity variable are shown to satisfy a set of Bethe-ansatz type equations similar to those obtained for the integrable XXZ chains. The eigenvalue for a filled sea of (N-1)-strings gives the free energy found by the matrix inversion method.