The scaling limit of two cluster boundaries in critical lattice models
Gamsa, Adam ; Cardy, John
arXiv, 0509004 / Harvested from arXiv
Text on arXiv
The probability that a point is to one side of a curve in Schramm-Loewner evolution (SLE) can be obtained alternatively using boundary conformal field theory (BCFT). We extend the BCFT approach to treat two curves, forming, for example, the left and right boundaries of a cluster. This proves to correspond to a generalisation to SLE(kappa,rho), with rho=2. We derive the probabilities that a given point lies between two curves or to one side of both. We find analytic solutions for the cases kappa=0,2,4,8/3,8. The result for kappa=6 leads to predictions for the current distribution at the plateau transition in the semiclassical approximation to the quantum Hall effect.
Publié le : 2005-09-02
Classification:  Mathematical Physics,  Condensed Matter - Statistical Mechanics 
@article{0509004,
     author = {Gamsa, Adam and Cardy, John},
     title = {The scaling limit of two cluster boundaries in critical lattice models},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0509004}
}

Gamsa, Adam; Cardy, John. The scaling limit of two cluster boundaries in critical lattice models. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0509004/