Extremal Fluctuations are Essential for Relaxation in Complex Energy Landscapes.

We determine the importance of extreme, record-sized events on the non-equilibrium relaxation ("aging") after a sudden quench into the glassy phase. Here, we directly measure the impact of extreme events on the evolving system in Monte Carlo simulations of Ising spin glasses and ferromagnets undergoing quenches into either a low or high-temperature phase. Our results show that, if we bar the attainment of new record-high energy fluctuations (by explicitly imposing a "lid" on the fluctuation spectrum), further relaxation in the low-temperature glassy phase is impeded markedly while in all other phases such a lid actually accelerates the relaxation process. Such rare record events, emerging naturally in the sequence of ordinary fluctuations of any relaxing system, thus prove to be key in activating the aging dynamics, as has been argued for systems like spin glasses, superconductors, gels, colloids, and granular piles. This dynamics of records succeeds in explaining the logarithmic decay of the free energy and the memory effects encoded in the scaling of two-time correlation functions of those aging systems. These findings are interpreted through the interplay of fluctuations and generic features of the hierarchical, complex energy landscape of glassy systems.