Criticality of the Anisotropic Quantum Heisenberg Model on a Self-Dual Hierarchical Lattice

Abstract
Within a real-space renormalization-group framework, the spin-½ 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.