J. Stein: Critical properties of a spin glass with anisotropic Dzyaloshinskii-Moriya interaction, J. Phys. A 29 (1996) 963 (Postscript-File)
We study the classical n-vector 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) X^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 eta and nu 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.