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Metastability in the dilute Ising model
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Bodineau, Thierry, Graham, Benjamin T. and Wouts, Marc (2013) Metastability in the dilute Ising model. Probability Theory and Related Fields, Volume 157 (Number 3-4). pp. 955-1009. doi:10.1007/s00440-012-0474-8 ISSN 0178-8051.
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Official URL: http://dx.doi.org/10.1007/s00440-012-0474-8
Abstract
Consider Glauber dynamics for the Ising model on the hypercubic lattice with a positive magnetic field. Starting from the minus configuration, the system initially settles into a metastable state with negative magnetization. Slowly the system relaxes to a stable state with positive magnetization. Schonmann and Shlosman showed that in the two dimensional case the relaxation time is a simple function of the energy required to create a critical Wulff droplet. The dilute Ising model is obtained from the regular Ising model by deleting a fraction of the edges of the underlying graph. In this paper we show that even an arbitrarily small dilution can dramatically reduce the relaxation time. This is because of a catalytic effect—rare regions of high dilution speed up the transition from minus phase to plus phase.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
| Library of Congress Subject Headings (LCSH): | Ising model, Stability, Hysteresis | ||||
| Journal or Publication Title: | Probability Theory and Related Fields | ||||
| Publisher: | Springer | ||||
| ISSN: | 0178-8051 | ||||
| Official Date: | 2013 | ||||
| Dates: |
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| Volume: | Volume 157 | ||||
| Number: | Number 3-4 | ||||
| Page Range: | pp. 955-1009 | ||||
| DOI: | 10.1007/s00440-012-0474-8 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access | ||||
| Funder: | France. Ministère de l'éducation nationale, France. Agence nationale de la recherche (ANR), Fondation Sciences Mathématiques de Paris | ||||
| Grant number: | 2010 BLAN 0108 01 (ANR) |
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