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We study the low temperature out of equilibrium Monte Carlo dynamics of thedisordered Ising $p$-spin Model with $p=3$ and a small number of spinvariables. We focus on sequences of configurations that are stable againstsingle spin flips obtained by instantaneous gradient descent from persistentones. We analyze the statistics of energy gaps, energy barriers and trappingtimes on sub-sequences such that the overlap between consecutive configurationsdoes not overcome a threshold. We compare our results to the predictions ofvarious trap models finding the best agreement with the step model when the$p$-spin configurations are constrained to be uncorrelated.

Barriers, trapping times and overlaps between local minima in the dynamics of the disordered Ising $p$-spin Model