Fredrickson - Andersen One Spin Facilitated Model out of Equilibrium
O. Blondel, N. Cancrini, F. Martinelli, C. Roberto, C. Toninelli
2013, v.19, Issue 3, 383-406
We consider the Fredrickson and Andersen one spin facilitated model (FA1f) on an infinite connected graph with polynomial growth. Each site with rate one refreshes its occupation variable to a filled or to an empty state with probability $p\in [0,1]$ or $q=1-p$ respectively, provided that at least one of its nearest neighbours is empty. We study the non-equilibrium dynamics started from an initial distribution $\nu$ different from the stationary product $p$-Bernoulli measure $\mu$. We assume that, under $\nu$, the distance between two nearest empty sites has exponential moments. We then prove convergence to equilibrium when the vacancy density $q$ is above a proper threshold $\bar q<1$. The convergence is exponential or stretched exponential, depending on the growth of the graph. In particular it is exponential on $\bbZ^d$ for $d=1$ and stretched exponential for $d>1$. Our result can be generalized to other non cooperative models.
Keywords: interacting particle systems,Fredrickson - Andersen model,convergence to equilibrium
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