Three-dimensional Heisenberg spin glass under a weak random anisotropy

We perform a finite-size scaling study of the three-dimensional Heisenberg spin glass in the presence of weak random anisotropic interactions, up to lattice sizes L = 32. Anisotropies have a major impact on the phase transition. The chiral-glass susceptibility does not diverge due to a large anomalous dimension. It follows that the anisotropic spin glass belongs to a Universality Class different from the isotropic model, which questions the applicability of the chirality scenario.