A comparative study of the magnetization process of two-dimensional antiferromagnets

Plateaux in the magnetization curves of the square-, triangular- and hexagonal-lattice spin-1/2 XXZ antiferromagnet are investigated. One finds a zero-magnetization plateau (corresponding to a spin gap) on the square and hexagonal lattice with Ising-like anisotropies, and a plateau with one-third of the saturation magnetization on the triangular lattice which survives a small amount of easy-plane anisotropy. Here we start with transfer-matrix computations for the Ising limit and continue with series in the XX Z anisotropy for plateau boundaries using the ground states of the Ising limit. The main focus is then a numerical computation of the magnetization curves with anisotropies in the vicinity of the isotropic situation. Finally, we discuss the universality class associated with the asymptotic behaviour of the magnetization curve close to saturation, as observed numerically in two and higher dimensions.