Off-equilibrium dynamics of a four-dimensional spin glass with asymmetric couplings

We study the off-equilibrium dynamics of the Edwards-Anderson spin glass in four dimensions under the influence of a non-Hamiltonian perturbation (i.e. with asymmetric couplings). We find that for small asymmetry the model behaves like the Hamiltonian model, while for large asymmetry the behaviour of the model can be well described by an interrupted ageing scenario. The autocorrelation function C(t(w) + tau, t(w)) scales as tau/tau(w)(beta), with beta a function of the asymmetry. For very long waiting times the previous regime crosses over to a time translational invariant regime with stretched exponential relaxation. The model does not show signs of reaching a time translational invariant regime for weak asymmetry, but in the ageing regime the exponent beta is always different from 1, showing a non-trivial ageing scenario also valid in the Hamiltonian model.