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Sharp thresholds for the random-cluster and Ising models
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Graham, Benjamin T. and Grimmett, Geoffrey (2011) Sharp thresholds for the random-cluster and Ising models. The Annals of Applied Probability, Vol.21 (No.1). pp. 240-265. doi:10.1214/10-AAP693 ISSN 1050-5164.
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Official URL: http://dx.doi.org/10.1214/10-AAP693
Abstract
A sharp-threshold theorem is proved for box-crossing probabilities on the square lattice. The models in question are the random-cluster model near the self-dual point psd(q)=√q∕(1+√q), the Ising model with external field, and the colored random-cluster model. The principal technique is an extension of the influence theorem for monotonic probability measures applied to increasing events with no assumption of symmetry.
| 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): | Probabilities, Ising model, Stochastic processes, Percolation (Statistical physics) | ||||
| Journal or Publication Title: | The Annals of Applied Probability | ||||
| Publisher: | Institute of Mathematical Statistics | ||||
| ISSN: | 1050-5164 | ||||
| Official Date: | 2011 | ||||
| Dates: |
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| Volume: | Vol.21 | ||||
| Number: | No.1 | ||||
| Page Range: | pp. 240-265 | ||||
| DOI: | 10.1214/10-AAP693 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published |
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