Phase diagram of the quantum anisotropic Heisenberg model on a self-dual hierarchical lattice.

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 framework. We extend the results to the antiferromagnetic case and show that T c vanishes for values of the anisotropy parameter Δ≤0.399, i.e., for small anisotropy the order is destroyed by quantum fluctuations at any finite temperature