Violation of the fluctuation-dissipation theorem in finite-dimensional spin glasses

We study the violation of the fluctuation-dissipation theorem in the three-and four-dimensional Gaussian Ising spin glasses using on and off equilibrium simulations. We have characterized numerically the function X(C) that determine the violation and we have studied its scaling properties. Moreover we have computed the function x(C) which characterize the breaking of the replica symmetry directly from equilibrium simulations. The two functions are numerically equal and in this way we have established that the conjectured connection between the violation of fluctuation-dissipation theorem in the off-equilibrium dynamics and the replica symmetry breaking at equilibrium holds for finite-dimensional spin glasses. These results point to a spin-glass phase with spontaneously broken replica symmetry in finite-dimensional spin glasses.