CUTOFF FOR THE SQUARE PLAQUETTE MODEL ON A CRITICAL LENGTH SCALE

• 成果类型: Article
• 署名作者: Chleboun, Paul; Smith, Aaron
• 署名单位: University of Warwick; University of Ottawa
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/20-AAP1601
• 发表日期: 2021
• 页码: 668-702
• 关键词: constrained ising process; mixing times; UNIVERSALITY; equilibrium; relaxation; torus

摘要

Plaquette models are short range ferromagnetic spin models that play a key role in the dynamic facilitation approach to the liquid glass transition. In this paper we study the dynamics of the square plaquette model at the smallest of the three critical length scales discovered in ( J. Stat. Phys. 169 (2017) 441-471). Our main result is that the plaquette model with periodic boundary conditions, on this length scale, exhibits a sharp transition in the convergence to equilibrium, known as cutoff. This substantially refines our coarse understanding of mixing from previous work (Chleboun and Smith (2018)). The basic approach is to reduce the problem to an analysis of the trace process on certain metastable states, which may be useful in proving cutoff in other situations.