  Trap models have been initially proposed as toy models for dynamical
relaxation in extremely simplified rough potential energy landscapes. Their
importance has considerably grown recently thanks to the discovery that the
trap like aging mechanism is directly controlling the out-of-equilibrium
relaxation processes of more sophisticated spin models, that are considered as
the solvable counterpart of real disordered systems. Establishing on a firmer
ground the connection between these spin model out-of-equilibrium behavior and
the trap like aging mechanism would shed new light on the properties, still
largely mysterious, of the activated out-of-equilibrium dynamics of disordered
systems. In this work we discuss numerical evidences of emergent trap-like
aging behavior in a variety of disordered models. Our numerical results are
backed by analytic derivations and heuristic discussions. Such exploration
reveals some of the tricks needed to analyze the trap behavior in spite of the
occurrence of secondary processes, of the existence of dynamical correlations
and of finite system's size effects.

Disordered Systems and Neural Networks