Critical properties and phase diagram of the quantum anisotropic XY spin   chain in a random magnetic field: A density-matrix renormalization-group   analysis
  The spin-1/2 quantum anisotropic XY spin chain in a transverse random magnetic field parallel to the z axis is numerically studied by means of the density-matrix renormalization group. The dependence of the spontaneous magnetization and the energy gap on both the strength of the random magnetic field and the factor of anisotropy is determined. The critical line for the order-disorder phase transition is obtained and the resulting phase diagram is drawn. Our results are compatible with the fact that models with different factors of anisotropy fall within the same universality class as the quantum Ising model in a transverse random field. 
A. Juozapavicius, L. Urba, S. Caprara and A. Rosengren