Sharp thresholds for the random-cluster and Ising models
Probability
2011-01-06 v2
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 , 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.
Cite
@article{arxiv.0903.1501,
title = {Sharp thresholds for the random-cluster and Ising models},
author = {Benjamin Graham and Geoffrey Grimmett},
journal= {arXiv preprint arXiv:0903.1501},
year = {2011}
}
Comments
Published in at http://dx.doi.org/10.1214/10-AAP693 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)