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

We apply density-matrix renormalization-group methods to study the phase diagram of the quantum axial next-nearest-neighbor Ising 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 βq=1∕2.