ADE and SLE

Details ADE and SLE ADE and SLE

2006-10-13

arxiv.org/abs/math-ph/0610030v2

J.Phys. A40 (2007) 1427-1438

Physics

Mathematical Physics

14 pages. v.2: minor additions

Scientific paper

10.1088/1751-8113/40/7/001

We point out that the probability law of a single domain wall separating clusters in ADE lattice models in a simply connected domain is identical to that of corresponding chordal curves in the lattice O(n) and Q-state Potts models, for suitable n or Q. They are conjectured to be described in the scaling limit by chordal SLE(kappa) with kappa rational and >2. However in a multiply-connected domain the laws can differ from those for the corresponding O(n) or Potts model. The correspondence also sheds light on the scaling limit of multiple curves.

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