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We apply Density Matrix Renormalization Group methods to study the phasediagram of the quantum ANNNI model in the region of low frustration where theferromagnetic coupling is larger than the next-nearest-neighborantiferromagnetic one. By Finite Size Scaling on lattices with up to 80 siteswe locate precisely the transition line from the ferromagnetic phase to aparamagnetic phase without spatial modulation. We then measure and analyze thespin-spin correlation function in order to determine the disorder transitionline where a modulation appears. We give strong numerical support to theconjecture that the Peschel-Emery one-dimensional line actually coincides withthe disorder line. We also show that the critical exponent governing thevanishing of the modulation parameter at the disorder transition is $\beta_q =1/2$.Comment: 4 pages, 5 eps figure

Density-matrix renormalization-group study of the disorder line in the quantum axial next-nearest-neighbor Ising model