Numerical evidences of universal trap-like aging dynamics

Abstract

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.

Activated dynamics of the Ising p-spin disordered model with finite number of variables

“…The straight line is log(t/t w ) and fits the long time-delay data very well. In the context of the TM, an equivalent correlation function which measures the probability that the system did not leave a trap between t w and t w + t can be computed exactly and is known as the "the Arcsin law", H x (w) [34,36]. Interestingly, the Arcsin law depends on the scaling variable w = t/t w , the same which we found to describe quite well the p-spin model ageing behaviour.…”

“…Interpreting the outcome of simulations of the REM and generalisations has proved to be a very complex task. Convincing evidence for an effective TM description emerges only when the observation times are scaled exponentially with system size N [36,42,43].…”

Activated aging dynamics and effective trap model description in the random energy model

“…Clearly much larger size and times would be needed to enter the asymptotic regime. Remarkably, a recent numerical study of generalised trap models [28] has shown that the very same problem also arises in simpler models with a gaussian distribution of energies. The analysis developed in [28] could be applied to the REM case in order to find more stringent evidences of trap dynamics.…”

“…Remarkably, a recent numerical study of generalised trap models [28] has shown that the very same problem also arises in simpler models with a gaussian distribution of energies. The analysis developed in [28] could be applied to the REM case in order to find more stringent evidences of trap dynamics. Finally in agreement with the results for the EREM, we find also in this case a more pronounced difference at low temperature between basin and configuration descriptions.…”

“…On each one of them the dynamics is effectively identical to the one of an exponential trap model with a time-scale dependent α [27]. More precisely, the continuous time dynamics of the GTM behaves like the one of a TM with a parameter α(t w ) = T /x(t w ) = N/(T log t w ) < 1 dependent on the age of the system [13] if the times at which the dynamics is observed are properly rescaled [11,13,28]. 2…”