April 2021 Cutoff for the square plaquette model on a critical length scale
Paul Chleboun, Aaron Smith
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Ann. Appl. Probab. 31(2): 668-702 (April 2021). DOI: 10.1214/20-AAP1601


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.


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Paul Chleboun. Aaron Smith. "Cutoff for the square plaquette model on a critical length scale." Ann. Appl. Probab. 31 (2) 668 - 702, April 2021. https://doi.org/10.1214/20-AAP1601


Received: 1 November 2019; Revised: 1 May 2020; Published: April 2021
First available in Project Euclid: 1 April 2021

Digital Object Identifier: 10.1214/20-AAP1601

Primary: 60J27
Secondary: 60J20

Keywords: Cutoff phenomenon , Glass transition , Markov chain , mixing time , plaquette model , spectral gap

Rights: Copyright © 2021 Institute of Mathematical Statistics


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Vol.31 • No. 2 • April 2021
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