KINETICALLY CONSTRAINED SPIN MODELS ON TREES

• 成果类型: Article
• 署名作者: Martinelli, F.; Toninelli, C.
• 署名单位: Roma Tre University; Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Universite Paris Cite
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/12-AAP891
• 发表日期: 2013
• 页码: 1967-1987
• 关键词: bootstrap percolation; ising-model; glauber dynamics

摘要

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 analyze KCSM on the regular lattice Z(d).