Crossover of the antiferromagnet Heisenberg to XY model

The criticality of the quantum anisotropic spin- Heisenberg antiferromagnetic model is studied by the mean-field renormalization group (MFRG) approach. The critical temperature and the thermal exponent for the ferromagnetic (F) and antiferromagnetic (AF) cases are obtained as a function of the anisotropy parameter on a three-dimensional lattice. Particular attention is drawn to the difference between Tc (F case) and TN (AF case). It is shown that in the quantum XY limit Tc=TN, whereas TN>Tc for the anisotropic Heisenberg model. We have also shown that the thermal critical exponent yt presents a small dependence on the type of interaction (F or AF) due to finite size effects.