  By means of the Density Matrix Renormalization Group technique, we have
studied the region where $XXZ$-like behavior is most likely to emerge within
the phase diagram of the F-AF anisotropic extended ($J-J'$) Heisenberg chain.
We have analyzed, in great detail, the equal-time two-spin correlation
functions, both in- and out-of- plane, as functions of the distance (and
momentum). Then, we have extracted, through an accurate fitting procedure, the
exponents of the asymptotic power-law decay of the spatial correlations. We
have used the exact solution of $XXZ$ model ($J'=0$) to benchmark our results,
which clearly show the expected agreement. A critical value of $J'$ has been
found where the relevant power-law decay exponent is independent of the
in-plane nearest-neighbor coupling.
