Exchange Stiffness and Macroscopic Anisotropy in Heisenberg Spin-Glasses

The consequences of rotational-symmetry breaking in Heisenberg spin-glasses are studied with use of order parameters which are time-dependent SO(3) rotation matrices. A microscopic derivation of the hydrodynamic "triad" theory, including the effect of small magnetic fields and random anisotropies, is presented. In the mean-field limit the finite-time exchange stiffness and macroscopic anisotropy constants vanish near the transition temperature $T_g$ as ${(T_g-T)}^{\mu }$, $\mu =3\mathrm{}$.