Sharp thresholds for the random-cluster and Ising models
Graham, Benjamin ; Grimmett, Geoffrey
Ann. Appl. Probab., Tome 21 (2011) no. 1, p. 240-265 / Harvested from Project Euclid
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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.
Publié le : 2011-02-15
Classification:  Random-cluster model,  Potts model,  Ising model,  percolation,  box-crossing,  influence,  sharp threshold,  colored random-cluster model,  fuzzy Potts model,  60K35,  82B20,  60E15 
@article{1292598033,
     author = {Graham, Benjamin and Grimmett, Geoffrey},
     title = {Sharp thresholds for the random-cluster and Ising models},
     journal = {Ann. Appl. Probab.},
     volume = {21},
     number = {1},
     year = {2011},
     pages = { 240-265},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1292598033}
}

Graham, Benjamin; Grimmett, Geoffrey. Sharp thresholds for the random-cluster and Ising models. Ann. Appl. Probab., Tome 21 (2011) no. 1, pp.  240-265. http://gdmltest.u-ga.fr/item/1292598033/