Rotational symmetry breaking in Heisenberg spin glasses: A microscopic approach.

We study the consequences of rotational symmetry breaking in isotropic vector spin glasses. Starting from a microscopic model we identify the underlying symmetries of time-dependent (replica-dependent) SO(rn) rotations. The hydrodynamic triad theory is confirmed and the spinwave stiffness is related to a generalized transverse susceptibility. An expansion around mean-field theory is used to calculate the stiffness approximately.