%0 Journal Article
%T Sharp thresholds for the random-cluster and Ising models
%A Benjamin Graham
%A Geoffrey Grimmett
%J Mathematics
%D 2009
%I arXiv
%R 10.1214/10-AAP693
%X 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 $p_{\mathrm {sd}}(q)=\sqrt{q}/(1+\sqrt{q})$, 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.
%U http://arxiv.org/abs/0903.1501v2