  We apply Density Matrix Renormalization Group methods to study the phase
diagram of the quantum ANNNI model in the region of low frustration where the
ferromagnetic coupling is larger than the next-nearest-neighbor
antiferromagnetic one. By Finite Size Scaling on lattices with up to 80 sites
we locate precisely the transition line from the ferromagnetic phase to a
paramagnetic phase without spatial modulation. We then measure and analyze the
spin-spin correlation function in order to determine the disorder transition
line where a modulation appears. We give strong numerical support to the
conjecture that the Peschel-Emery one-dimensional line actually coincides with
the disorder line. We also show that the critical exponent governing the
vanishing of the modulation parameter at the disorder transition is $\beta_q =
1/2$.
