Study of the phase transition in the 3D Ising spin glass from out-of-equilibrium numerical simulations

Using the decay of the out- of- equilibrium spin - spin correlation function we compute the equilibrium Edward - Anderson order parameter in the threedimensional binary Ising spin glass in the spin glass phase. We have checked that the Edward - Anderson order parameter computed from out- of-equilibrium numerical simulations follows with good precision the critical law as determined in experiments and in numerical studies at equilibrium ( which allow us to estimate the beta critical exponent). Finally, we present a large time study of the off- equilibrium fluctuation - dissipation relations and find strong discrepancies ( in the low-temperature region) between the numerical data and the droplet theory predictions and agreement with the predictions of the replica symmetry breaking theory.