Open Access
2020 Mixing of the square plaquette model on a critical length scale
Paul Chleboun, Aaron Smith
Electron. J. Probab. 25: 1-53 (2020). DOI: 10.1214/20-EJP487


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 [7]. Our main results are estimates of the spectral gap and mixing time for two natural boundary conditions. As a consequence, we observe that these time scales depend heavily on the boundary condition in this scaling regime.


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Paul Chleboun. Aaron Smith. "Mixing of the square plaquette model on a critical length scale." Electron. J. Probab. 25 1 - 53, 2020.


Received: 14 October 2019; Accepted: 27 June 2020; Published: 2020
First available in Project Euclid: 6 August 2020

zbMATH: 07252721
MathSciNet: MR4136469
Digital Object Identifier: 10.1214/20-EJP487

Primary: 60J27 , 60J28

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

Vol.25 • 2020
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