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Mixing time bounds for oriented kinetically constrained spin models


 
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1. Title Title of document Mixing time bounds for oriented kinetically constrained spin models
 
2. Creator Author's name, affiliation, country Paul Chleboun; University of Warwick; United Kingdom
 
2. Creator Author's name, affiliation, country Fabio Martinelli; Università Roma Tre; Italy
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) North-East model, kinetically constrained spin models, mixing time
 
3. Subject Subject classification 60J10,60J27,60J28
 
4. Description Abstract

We analyze the mixing time of a class of oriented kinetically constrained spin models (KCMs) on a d-dimensional lattice of n sites. A typical example is the North-East model, a 0-1 spin system on the two-dimensional integer lattice that evolves according to the following rule: whenever a site’s southerly and westerly nearest neighbours have spin 0, with rate one it resets its own spin by tossing a p-coin, at all other times its spin remains frozen. Such models are very popular in statistical physics because, in spite of their simplicity, they display some of the key features of the dynamics of real glasses. We prove that the mixing time is O(n log n) whenever the relaxation time is O(1). Our study was motivated by the “shape” conjecture put forward by G. Kordzakhia and S.P. Lalley.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) European Research Council
 
7. Date (YYYY-MM-DD) 2013-07-12
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/2516
 
10. Identifier Digital Object Identifier 10.1214/ECP.v18-2516
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 18
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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