K. Isler et Mb. Paranjape, VIOLATIONS OF THE STRING HYPOTHESIS IN THE SOLUTIONS OF THE BETHE-ANSATZ EQUATIONS IN THE XXX-HEISENBERG MODEL, Physics letters. Section B, 319(1-3), 1993, pp. 209-214
We study the equations for the quasi-momenta in the Bethe ansatz for t
he XXX-Heisenberg model. We show in a simple analytical fashion, that
the usual ''string hypothesis'' incorrectly predicts the number of rea
l solutions and the number of complex solutions for N > 21 in the sect
or with two spins flipped, confirming the work of Essler et al. We als
o introduce a new set of variables which allows the equations to be wr
itten as a single polynomial equation in one variable. We consider in
some detail the case of three spins flipped.