Absence of ageing in the remanent magnetization in Migdal-Kadanoff spin glasses

We study the non-equilibrium behaviour of three-dimensional spin glasses in the Migdal-Kadanoff approximation. This approximation is exact for disordered hierarchical lattices which have a unique ground state and equilibrium properties correctly described by the droplet model. Extensive numerical simulations show that this model lacks ageing in the remanent magnetization as well as a maximum in the magnetic viscosity in disagreement with experiments as well as with numerical studies of the Edwards-Anderson model. This result strongly limits the validity of the droplet model (at least in its simplest form) as a good model for real spin glasses. (author)