The scaling limit of two cluster boundaries in critical lattice models

Details The scaling limit of two cluster boundaries in critical lattice models The scaling limit of two cluster boundaries in critical lattice models

2005-09-02

arxiv.org/abs/math-ph/0509004v2

J. Stat. Mech. (2005) P12009

Physics

Mathematical Physics

27 pages, 7 figures

Scientific paper

10.1088/1742-5468/2005/12/P12009

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.

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