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Fredrickson-Andersen one spin facilitated model out of equilibrium | | Oriane Blondel
; Nicoletta Cancrini
; Fabio Martinelli
; Cyril Roberto
; Cristina Toninelli
; | | Date: |
21 May 2012 | | Abstract: | 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 $pin[0,1]$ 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 $
u$ different from the stationary product
$p$-Bernoulli measure $mu$. We assume that, under $
u$, the mean distance
between two nearest empty sites is uniformly bounded. We then prove convergence
to equilibrium when the vacancy density $q$ is above a proper threshold $ar
q<1$. The convergence is exponential or stretched exponential, depending on the
growth of the graph. In particular it is exponential on $bZ^d$ for $d=1$ and
stretched exponential for $d>1$. Our result can be generalized to other non
cooperative models. | | Source: | arXiv, 1205.4584 | | Services: | Forum | Review | PDF | Favorites | |
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