  Memory and rejuvenation effects in the magnetic response of off-equilibrium
spin glasses have been widely regarded as the doorway into the experimental
exploration of ultrametricity and temperature chaos (maybe the most exotic
features in glassy free-energy landscapes). Unfortunately, despite more than
twenty years of theoretical efforts following the experimental discovery of
memory and rejuvenation, these effects have thus far been impossible to
simulate reliably. Yet, three recent developments convinced us to accept this
challenge: first, the custom-built Janus II supercomputer makes it possible to
carry out "numerical experiments" in which the very same quantities that can be
measured in single crystals of CuMn are computed from the simulation, allowing
for parallel analysis of the simulation/experiment data. Second, Janus II
simulations have taught us how numerical and experimental length scales should
be compared. Third, we have recently understood how temperature chaos
materializes in aging dynamics. All three aspects have proved crucial for
reliably reproducing rejuvenation and memory effects on the computer. Our
analysis shows that (at least) three different length scales play a key role in
aging dynamics, while essentially all theoretical analyses of the aging
dynamics emphasize the presence and the crucial role of a single glassy
correlation length.
