Facilitated oriented spin models:some non equilibrium results

Abstract : We analyze the relaxation to equilibrium for kinetically constrained spin models (KCSM) when the initial distribution $\nu$ is different from the reversible one, $\mu$. This setting has been intensively studied in the physics literature to analyze the slow dynamics which follows a sudden quench from the liquid to the glass phase. We concentrate on two basic oriented KCSM: the East model on $\bbZ$, for which the constraint requires that the East neighbor of the to-be-update vertex is vacant and the model on the binary tree introduced in \cite{Aldous:2002p1074}, for which the constraint requires the two children to be vacant. While the former model is ergodic at any $p\neq 1$, the latter displays an ergodicity breaking transition at $p_c=1/2$. For the East we prove exponential convergence to equilibrium with rate depending on the spectral gap if $\nu$ is concentrated on any configuration which does not contain a forever blocked site or if $\nu$ is a Bernoulli($p'$) product measure for any $p'\neq 1$. For the model on the binary tree we prove similar results in the regime $p,p'
Type de document :
Pré-publication, Document de travail
16 pages. 2008
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Contributeur : Cristina Toninelli <>
Soumis le : vendredi 24 octobre 2008 - 10:51:07
Dernière modification le : mercredi 12 octobre 2016 - 01:02:19


  • HAL Id : hal-00333798, version 1
  • ARXIV : 0810.4237




Nicoletta Cancrini, Fabio Martinelli, Roberto H. Schonmann, Cristina Toninelli. Facilitated oriented spin models:some non equilibrium results. 16 pages. 2008. <hal-00333798>



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