  We apply a recently developed functional renormalization group (fRG) scheme
for quantum spin systems to the spin-1/2 antiferromagnetic XXZ model on a
two-dimensional square lattice. Based on an auxiliary fermion representation we
derive flow equations which allow a resummation of the perturbation series in
the spin-spin interactions. Spin susceptibilities are calculated for different
values of the anisotropy parameter. The phase transition between planar and
axial ordering at the isotropic point is reproduced correctly. The results for
the critical scales from the fRG as quantitative measures for the ordering
temperatures are in good agreement with the exact solution in the Ising limit.
On the easy-plane side, the deviations from critical temperatures obtained with
quantum Monte Carlo are larger but still acceptable. However, at the isotropic
point the Mermin-Wagner theorem is violated such that a precise description of
the behavior in the vicinity of the phase transition is not possible. We
discuss possible reasons for these discrepanies.
