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Relaxation Mechanisms in Glassy Dynamics: the Arrhenius and Fragile Regimes

Generic glass formers exhibit at least two characteristic changes in their relaxation behavior, first to an Arrhenius-type relaxation at some characteristic temperature, and then at a lower characteristic temperature to a super-Arrhenius (fragile) behavior. We address these transitions by studying the statistics of free energy barriers for different systems at different temperatures and space dimensions. We present a clear evidence for changes in the dynamical behavior at the transition to Arrhenius and then to a super-Arrhenius behavior. A simple model is presented, based on the idea of competition between single-particle and cooperative dynamics. We argue that Arrhenius behavior can take place as long as there is enough free volume for the completion of a simple $T_1$ relaxation process. Once free volume is absent one needs a cooperative mechanism to `collect' enough free volume. We show that this model captures all the qualitative behavior observed in simulations throughout the considered temperature range.