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Cutoff for the square plaquette model on a critical length scale

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Chleboun, Paul and Smith, Aaron (2021) Cutoff for the square plaquette model on a critical length scale. Annals of Applied Probability, 31 (2). pp. 668-702. doi:10.1214/20-AAP1601

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Official URL: https://doi.org/10.1214/20-AAP1601

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Abstract

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 [6].
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 [7]. 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.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Statistics
Library of Congress Subject Headings (LCSH): Markov processes, Glass transition temperature, Probabilities, Mathematical physics
Journal or Publication Title: Annals of Applied Probability
Publisher: Institute of Mathematical Statistics
ISSN: 1050-5164
Official Date: 1 April 2021
Dates:
DateEvent
1 April 2021Available
16 June 2020Accepted
Volume: 31
Number: 2
Page Range: pp. 668-702
DOI: 10.1214/20-AAP1601
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Copyright Holders: Copyright © 2021 Institute of Mathematical Statistics
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
UNSPECIFIED[NSERC] Natural Sciences and Engineering Research Council of Canadahttp://dx.doi.org/10.13039/501100000038
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