Within a real-space renormalization-group framework, the spin-\textonehalf{} Heisenberg ferromagnet in the presence of an Ising-like anisotropy on a self-dual hierarchical lattice is discussed. The results are exact for this lattice but can also be considered as a quite satisfactory approximation for the simple square one. The controversial point on how
Tc vanishes in the isotropic Heisenberg limit is analyzed: Quite strong evidence is presented favoring a continuous function of anisotropy. The crossover from the isotropic Heisenberg model to the pure Ising one is exhibited.
A good approximation for the phase diagram of the quantum anisotropic spin-1/2 Heisenberg ferromagnet on a self-dual hierarchical lattice is calculated within a real-space renormalization-group frame-work. We extend the results to the antiferromagnetic case and show that
Tc vanishes for values of the anisotropy parameter \ensuremath{\Delta}\ensuremath{\le}0.399, i.e., for small anisotropy the order is destroyed by quantum fluctuations at any finite temperature.