Sharp thresholds for the random-cluster and Ising models
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. ISSN 1050-5164Full text not available from this repository.
Official URL: http://dx.doi.org/10.1214/10-AAP693
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
|Divisions:||Faculty of 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|
|Page Range:||pp. 240-265|
 AIZENMAN, M.,BARSKY, D. J. and FERNÁNDEZ, R. (1987). The phase transition in a general
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