Kinetically constrained spin models on trees

Abstract : We analyze kinetically constrained 0-1 spin models (KCSM) on rooted and unrooted trees of finite connectivity. We focus in particular on the class of Friedrickson Andersen models FA-jf and on an oriented version of them. These tree models are particularly relevant in physics literature since some of them undergo an ergodicity breaking transition with the mixed first-second order character of the glass transition. Here we first identify the ergodicity regime and prove that the critical density for FA-jf and OFA-jf models coincide with that of a suitable bootstrap percolation model. Next we prove for the first time positivity of the spectral gap in the whole ergodic regime via a novel argument based on martingales ideas. Finally, we discuss how this new technique can be generalized to analyse KCSM on the regular lattice Zd.
Type de document :
Pré-publication, Document de travail
2012
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https://hal.archives-ouvertes.fr/hal-00705259
Contributeur : Cristina Toninelli <>
Soumis le : jeudi 7 juin 2012 - 11:06:09
Dernière modification le : mardi 11 octobre 2016 - 13:52:06

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  • HAL Id : hal-00705259, version 1
  • ARXIV : 1202.3907

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UPMC | INSMI | PMA | USPC

Citation

F. Martinelli, C. Toninelli. Kinetically constrained spin models on trees. 2012. <hal-00705259>

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