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.
Citation
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