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.
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https://hal.archives-ouvertes.fr/hal-00705259
Contributor : Cristina Toninelli <>
Submitted on : Thursday, June 7, 2012 - 11:06:09 AM
Last modification on : Thursday, March 21, 2019 - 1:05:57 PM

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

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

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