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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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WRAP-cutoff-square-plaquette-model-critical-length-scale-Chleboun-2020.pdf - Accepted Version - Requires a PDF viewer. Download (1330Kb) | Preview |
Official URL: https://doi.org/10.1214/20-AAP1601
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 | ||||||
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| 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: |
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| 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: |
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