Conformal invariance in random cluster models. II. Full scaling limit as a branching SLE
Kemppainen, Antti ; Smirnov, Stanislav
arXiv, 1609.08527 / Harvested from arXiv
Text on arXiv
In the second article of this series, we establish the convergence of the loop ensemble of interfaces in the random cluster Ising model to a conformal loop ensemble (CLE) --- thus completely describing the scaling limit of the model in terms of the random geometry of interfaces. The central tool of the present article is the convergence of an exploration tree of the discrete loop ensemble to a branching SLE$(16/3,-2/3)$. Such branching version of the Schramm's SLE not only enjoys the locality property, but also arises logically from the Ising model observables.
Publié le : 2016-09-27
Classification:  Mathematical Physics,  Mathematics - Probability 
@article{1609.08527,
     author = {Kemppainen, Antti and Smirnov, Stanislav},
     title = {Conformal invariance in random cluster models. II. Full scaling limit as
  a branching SLE},
     journal = {arXiv},
     volume = {2016},
     number = {0},
     year = {2016},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1609.08527}
}

Kemppainen, Antti; Smirnov, Stanislav. Conformal invariance in random cluster models. II. Full scaling limit as
  a branching SLE. arXiv, Tome 2016 (2016) no. 0, . http://gdmltest.u-ga.fr/item/1609.08527/