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 ∈ [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 ν different from the stationary product p-Bernoulli measure µ. We assume that, under ν, 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 q <¯ 1. The convergence is exponential or stretched exponential, depending on the growth of the graph. In particular it is exponential on Z d for d = 1 and stretched exponential for d > 1. Our result can be generalized to other non cooperative models.

Blondel, O., Cancrini, N., Martinelli, F., Roberto, C., Toninelli, C. (2013). Fredrickson-Andersen one spin facilitated model out of equilibrium. MARKOV PROCESSES AND RELATED FIELDS, 19(3), 383-406.

Fredrickson-Andersen one spin facilitated model out of equilibrium.

MARTINELLI, Fabio;
2013-01-01

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 p ∈ [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 ν different from the stationary product p-Bernoulli measure µ. We assume that, under ν, 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 q <¯ 1. The convergence is exponential or stretched exponential, depending on the growth of the graph. In particular it is exponential on Z d for d = 1 and stretched exponential for d > 1. Our result can be generalized to other non cooperative models.
2013
Blondel, O., Cancrini, N., Martinelli, F., Roberto, C., Toninelli, C. (2013). Fredrickson-Andersen one spin facilitated model out of equilibrium. MARKOV PROCESSES AND RELATED FIELDS, 19(3), 383-406.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/116494
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