Dynamics near the spin-glass transition

We examine spin dynamics just above a spin-glass transition for two classical soft-spin models with random exchange interactions. The statics of the two models are identical; in mean-field theory we find an Edwards-Anderson transition of the usual sort. The dynamics are described by Langevin equations: in one case we use a purely dissipative equation of motion for a nonconserved scalar spin, while in the other we include a "mode-coupling" term to describe the precession of a vector spin in the field of its neighbors and impose conservation of the total spin. In the first case we find critical slowing down as the transition at T₆ is approached from above (and t^-1{2} tails below T₆), in agreement with the result of Ma and Rudnick for a different model. In the second case, we find a divergent spin-diffusion constant: D (T-{T₆) }^-1{2} (d>4) and D (T-{T₆) }^2{d-1} (2<d<4), in agreement with our previous calculation for a mode-coupling version of the Ma-Rudnick model.