The frustrated antiferromagnetic Heisenberg model in the presence of a uniform field

On the basis of a numerical computation of the ground states in the sectors with a given total spin S we study the magnetic properties of the one-dimensional frustrated antiferromagnetic Heisenberg model at zero temperature and at the spin-fluid-dimer phase transition. We find that the magnetization curve M(B) has a quartic-root singularity near saturation, B --> 4. The longitudinal spin-spin, the dimer-dimer and the transverse spin-spin structure factors develop singularities at the field-dependent momenta p = p(3)(M) = pi(1 - 2M) and p = p(1)(M) = 2 pi M, respectively. The type of each of these singularities depends on the frustration parameter and the magnetization M.