We investigate the large N behavior of the complex solutions for the two magnon system in the S=1/2 Heisenberg XXZ model. The Bethe ansatz equations are numerically solved for the string solutions with new iteration method. A clear evidence of the violation of the string configurations is found at N = 22, 62, 121, 200, 299, 417, but the broken states are still Bethe states. The number of the Bethe states is consistent with the exact diagonalization, except one singular state.

It is shown that the continuum limit of the spin 1/2 Heisenberg XYZ model is far from sufficient for the site number of 16. Therefore, the energy spectrum of the XYZ model obtained by Kolanovic et al. has nothing to do with the massive Thirring model, but it shows only the spectrum of the finite size effects.The spin 1/2 Heisenberg model is a rich theory, which contains a variety of field theories in the continuum limit. In particular, the Heisenberg XYZ model is proved to be equivalent to the massive Thirring model in the continuum limit.Recently, Kolanovic, Pallua and Prester [1] solved the Heisenberg XYZ model numerically to study the bound state problem in the massive Thirring model. In

The Bethe ansatz equations for the spin 1/2 Heisenberg XXZ spin chain are numerically solved, and the energy eigenvalues are determined for the anti-ferromagnetic case.We examine the relation between the XXZ spin chain and the Thirring model, and show that the spectrum of the XXZ spin chain is different from that of the regularized Thirring model.