Universality and extremal aging for dynamics of spin glasses on subexponential time scales

We consider random hopping time (RHT) dynamics of the Sherrington‐Kirkpatrick (SK) model and p‐spin models of spin glasses. For any of these models and for any inverse temperature β > 0 we prove that, on time scales that are subexponential in the dimension, the properly scaled clock process (time‐change process) of the dynamics converges to an extremal process. Moreover, on these time scales, the system exhibits aging‐like behavior, which we call extremal aging. In other words, the dynamics of these models ages as the random energy model (REM) does. Hence, by extension, this confirms Bouchaud's REM‐like trap model as a universal aging mechanism for a wide range of systems that, for the first time, includes the SK model. © 2011 Wiley Periodicals, Inc.