Aging in correlation functions

We review the most striking experimental results on aging in a variety of disordered systems, which reveal similar features but also important differences. We argue that a generic model that reproduce many of these features is that of pinned defects in a disordered environment, hoping between different metastable states. The fact that energy barriers grow with the size of the reconforming regions immediately leads to a strong hierarchy of time scales. In particular, long wavelength glassy, aging modes and short wavelength equilibrated modes coexist in the system and offer a simple mechanism to explain the rejuvenation/memory effect, which does not rely on 'chaos' with temperature. These properties can be discussed within simplified models (such as the Sinai model) where the dynamics of the whole pinned object is reduced to that of its center of mass in a disordered potential. While the experiments in random ferromagnet-like systems can be satisfactorily accounted for, the correct picture for the aging dynamics of spin-glasses is still missing. Following recent ideas of Houdayer and Martin, we propose the idea that the ordered phase a spin-glass contains a large number of pinned, zero tension walls. Finally, we briefly discuss the status of the mean-field theories of aging.