  We perform a finite size analysis of the longitudinal and transverse
structure factors $S_j(p,\gamma,N),j=1,3$ in the groundstate of the
spin-$\frac{1}{2}$ XXZ model. Comparison with the exact results of Tonegawa for
the XX model yields excellent agreement. Comparison with the conjecture of
M\"uller, Thomas, Puga and Beck reveals discrepancies in the momentum
dependence of the longitudinal structure factors.
