Field-induced phase transition in the quantum Heisenberg antiferromagnetic model

Abstract The criticality of the quantum anisotropic spin- 1 2 Heisenberg antiferromagnetic model in the presence of a magnetic field is studied by mean field approximation. The critical temperature (TN) is obtained as a function of anisotropy parameter η (where η=1 and 0 correspond the isotropic Heisenberg and Ising models, respectively) and magnetic field on a three-dimensional lattice (d=3). Particular attention is draw to the influence of quantum effect in the phase diagram of the Heisenberg metamagnet (η=1). It is shown that quantum influence does not modify the critical field, where in the limit T=0 the results correspond the exact result hc=zJ, i.e., hc is independent of the anisotropy parameter η.