TRANSFORMATION OF THE BETHE EQUATIONS FOR FINITE CYCLES INTO SECULAR POLYNOMIALS IN ENERGY

The study of spin Hamiltonians is facilitated by the use of the Bethe equations. Up to now, these equations were primarily used for the stud y of the energy of the lowest state of a given symmetry. In this paper , we would like to show that there is a technique by which these equat ions for finite cycles can be transformed into an algebraic equation f or the energy in which the coefficients are polynomials in the couplin g constant, or just numbers.From this algebraic equation, we can get a ll energies of a given symmetry in a straightforward way.