The three-dimensional quantum Heisenberg ferromagnet with random anisotropy

Abstract
The authors study the critical properties of the 3D quantum Heisenberg ferromagnet with random anisotropies; that is, the coupling between any pair of nearest-neighbouring spins can be either isotropic (Heisenberg) or anisotropic (Ising-or XY-like) at random. Within a Migdal-Kadanoff approximation they obtain the full critical frontier and correlation length critical exponents. They found that the isotropic Heisenberg model is unstable (in the context of universality classes) in the presence of a small concentration of couplings with lower symmetry.