  We investigate the thermodynamic limit of the one-dimensional ferromagnetic
XXZ model with twisted (or antiperiodic ) boundary condition. It is shown that
the distribution of the Bethe roots of the inhomogeneous Bethe Ansatz equations
(BAEs) for the ground state as well as for the low-lying excited states satisfy
the string hypothesis, although the inhomogeneous BAEs are not in the standard
product form which has made the study of the corresponding thermodynamic limit
nontrivial. We also obtain the twisted boundary energy induced by the
non-trivial twisted boundary conditions in the thermodynamic limit.
