Critical properties of a spin glass with anisotropic Dzyaloshinskii–Moriya interaction

We study the classical n-vector (n > 3) spin glass with anisotropic quenched random Dzyaloshinskii–Moriya (DM) interaction. A random DM interaction with m independent and separated couplings defines a generalized gauge-glass model with a O(n − 2m) ⊗m O(2) rotational symmetry and a broken global reflection invariance. It is shown that this model is in the same universality class as the random-gauge XY (‘gauge glass’) model. With an additional uniaxial anisotropy, a crossover from Ising-like to gauge-glass critical behaviour is found for a sufficiently large variance of the DM interaction. A new situation arises when there is correlation between the separated random DM couplings. We show that the critical behaviour of a spin glass with two correlated couplings of the anisotropic DM interaction is in a new universality class. The critical exponents η and ν of this model are calculated at two-loop order near six dimensions. We also present a simplified and more rigorous field-theoretic analysis of the gauge-glass model.