A comparative study of the dynamics of inherent structures at low temperatures is performed on different models of glass formers: a three dimensional Lennard-Jones binary mixture (LJBM), facilitated spin models (either symmetrically constrained, SCIC, or asymmetrically, ACIC) and the trap model. We use suitable correlation functions introduced in a previous work which allow to distinguish the behaviour between models with or without spatial or topological structure. Furthermore, the correlations between inherent structures behave differently in the cases of strong (SCIC) and fragile (ACIC, LJBM) glasses, as a consequence of the different role played by energy barriers when the temperature is lowered. The similarities in the behaviour of the ACIC and LJBM suggest a common nature of the glassy dynamics for both systems.

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