Universality results for interacting particle systems with dynamical constraints
We introduce the kinetically constrained models (KCM), a class of interacting particle systems with a simple spin flip dynamics subject to local dynamical constraints. Each vertex is resampled (independently) at rate one by tossing a (1-q)-coin iff a certain neighbourhood of the vertex contains no particles. In other words, the holes (empty vertices) act as facilitating sites. When q shrinks to 0, the presence of the constraints gives rise to glassy dynamics, in particular to an anomalous divergence of the characteristic time scales. Thus, KCM are extensively used in physics literature to model the liquid-glass transition, a longstanding open problem in condensed matter physics.
We focus on the behavior of E(T_0), the mean over the stationary process of the first time at which the origin becomes empty. Our results establish the universality classes of KCM in two dimensions: we group all possible constraints into distinct classes with all models in a class featuring the same divergence for E(T_0) as q->0. Within each class, we present an efficient relaxation mechanism that involves the cooperative motion of large rare patches of empty sites and we use it to determine matching upper and lower bounds for E(T_0).
Joint work with L.Marêché, I.Hartarsky, F.Martinelli and R.Morris
Sharp threshold for the FA-2f kinetically constrained model
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