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 1050-5164

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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
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
ISSN:	1050-5164
Date:	2011
Volume:	Vol.21
Number:	No.1
Page Range:	pp. 240-265
Identification Number:	10.1214/10-AAP693
Status:	Peer Reviewed
Publication Status:	Published
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URI:	http://wrap.warwick.ac.uk/id/eprint/41073

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