Sharp threshold for the FA-2f kinetically constrained model

• 成果类型: Article
• 署名作者: Hartarsky, Ivailo; Martinelli, Fabio; Toninelli, Cristina
• 署名单位: Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Roma Tre University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-022-01169-2
• 发表日期: 2023
• 页码: 993-1037
• 关键词: bootstrap percolation; spin models; ising-model; UNIVERSALITY; DYNAMICS

摘要

The Fredrickson-Andersen 2-spin facilitated model on Z(d) (FA-2f) is a paradigmatic interacting particle system with kinetic constraints (KCM) featuring dynamical facilitation, an important mechanism in condensed matter physics. In FA-2f a site may change its state only if at least two of its nearest neighbours are empty. Although the process is reversible w.r.t. a product Bernoulli measure, it is not attractive and features degenerate jump rates and anomalous divergence of characteristic time scales as the density q of empty sites tends to 0. A natural random variable encoding the above features is tau(0), the first time at which the origin becomes empty for the stationary process. Our main result is the sharp threshold tau(0 )= exp(d.lambda(d,2)+o(1)/q(1/(d-1)))w.h.p. with lambda(d,2) the sharp threshold constant for 2-neighbour bootstrap percolation on Z(d), the monotone deterministic automaton counterpart of FA-2f. This is the first sharp result for a critical KCM and it compares with Holroyd's 2003 result on bootstrap percolation and its subsequent improvements. It also settles various controversies accumulated in the physics literature over the last four decades. Furthermore, our novel techniques enable completing the recent ambitious program on the universality phenomenon for critical KCM and establishing sharp thresholds for other two-dimensional KCM.