Finite-size effects in a mean-field kinetically constrained model.
On the example of a Fredrickson-Andersen kinetically constrained model defined on the complete graph, we focus on the known property that equilibrium dynamics takes place at a first-order dynamical phase transition point in the space of time-realizations. We investigate the finite-size properties of this first order transition. By discussing and exploiting a mapping of the classical dynamical transition ? an argued signature of dynamical heterogeneities ? to a first-order quantum transition, we show that the quantum analogy can be exploited to extract finite-size properties, which in many respects are similar to those in genuine mean-field quantum systems with a first-order transition. The results shed light on anomalous features of distributions of history-dependent observables in models of glasses.
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