Sharp Thresholds for the Random-cluster and Ising Models
نویسندگان
چکیده
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 coloured 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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تاریخ انتشار 2009