  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.
