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, . The longitudinal spin - spin, the dimer - dimer and the transverse spin - spin structure factors develop singularities at the field-dependent momenta and , respectively. The type of each of these singularities depends on the frustration parameter and the magnetization M.
We analyze the thermodynamic properties of the spin-
S two-dimensional quantum Heisenberg antiferromagnet on a square lattice with nearest and next-nearest neighbor couplings in the N\'eel phase
(J2∕J1<0.4) employing the quantum hierarchical reference theory, a nonperturbative implementation of the renormalization group method to quantum systems. We investigate the staggered susceptibility, the structure factors, and the correlation length at finite temperature and for different values of the frustration ratio. From the finite temperature results, we also extrapolate ground state properties, such as spin stiffness and spontaneous staggered magnetization, providing an estimate of the extent of quantum corrections. The behavior of these quantities as a function of frustration may provide some hints on the breakdown of the N\'eel phase at zero temperature for larger values of
J2.