On the stability of the mean-field spin glass broken phase under non-Hamiltonian perturbations

We study the dynamics of the SK model modified by a small non-Hamiltonian perturbation. We study aging, and we find that on the timescales investigated by our numerical simulations it survives a small perturbation (and is destroyed by a large one). If we assume that we are observing a transient behaviour, the scaling of correlation times versus the asymmetry strength is not compatible with the one expected for the spherical model. We discuss the slow power law decay of observable quantities to equilibrium, and we show that for small perturbations power-like decay is preserved. We also discuss the asymptotically large time region on small lattices.

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