Response to a field of the $D=3$ Ising spin glass with Janus and JanusII dedicated computers

Using the Janus dedicated computer, and its new generation JanusII, we study the linear response to a field of the Edwards-Anderson model for times that cover twelve orders of magnitude. The fluctuation-dissipation relations are investigated for several values of $t_{\mathrm{w}}$. We observe that the violations of the fluctuation-dissipation theorem can be directly related to the $P(q)$ measured in equilibrium at finite sizes, although a simple statics-dynamics dictionary $L\leftrightarrow \xi(t_{\mathrm{w}})$ is not enough to account for the behavior at large times. We show that the equivalence can be easily restored by taking into account the growth of $\xi(t+t_{\mathrm{w}})$. Interestingly, experimental measurements of the spin glass correlation length rely precisely on the response of a spin glass to a field, although a direct relation between the measured object and the real $\xi$ has never been established. In this work, we mimic the experimental protocol with Janus data, which lets us relate the experimental $\xi$ with the length extracted from the spatial correlation function. These results allow us for the first time to make a quantitative comparison between experiments and simulations, finding a surprising good agreement with measurements in superspin glasses.