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February 2011 Sharp thresholds for the random-cluster and Ising models
Benjamin Graham, Geoffrey Grimmett
Ann. Appl. Probab. 21(1): 240-265 (February 2011). DOI: 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.

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Benjamin Graham. Geoffrey Grimmett. "Sharp thresholds for the random-cluster and Ising models." Ann. Appl. Probab. 21 (1) 240 - 265, February 2011. https://doi.org/10.1214/10-AAP693

Information

Published: February 2011
First available in Project Euclid: 17 December 2010

zbMATH: 1223.60081
MathSciNet: MR2759201
Digital Object Identifier: 10.1214/10-AAP693

Subjects:
Primary: 60E15, 60K35, 82B20

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.21 • No. 1 • February 2011
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