Conformal Invariance for Certain Models of the Bond-Triangular Type

Details Conformal Invariance for Certain Models of the Bond-Triangular Type Conformal Invariance for Certain Models of the Bond-Triangular Type

2007-10-18

arxiv.org/abs/0710.3446v4

Physics

Mathematical Physics

This paper has been withdrawn as its contents - with the exception of the Appendix on uniform continuity of crossing probabili

Scientific paper

Following the approach outlined in [18], convergence to SLE6 of the Exploration Processes for the correlated bond-triangular type models studied in [7] is established. This puts the said models in the same universality class as the standard site percolation model on the triangular lattice [19]. The result is proven for all domains with boundary (upper) Minkowski dimension less than two. Moreover, the proof of convergence applies in the general context of critical 2D percolation models, under the stipulation that Cardy's Formula can be established.

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