Cardy's Formula for Certain Models of the Bond-Triangular Type

Details Cardy's Formula for Certain Models of the Bond-Triangular Type Cardy's Formula for Certain Models of the Bond-Triangular Type

2006-01-11

arxiv.org/abs/math-ph/0601023v2

Physics

Mathematical Physics

49 pages, 7 figures

Scientific paper

10.1142/S0129055X0700305X

We introduce and study a family of 2D percolation systems which are based on the bond percolation model of the triangular lattice. The system under study has local correlations, however, bonds separated by a few lattice spacings act independently of one another. By avoiding explicit use of microscopic paths, it is first established that the model possesses the typical attributes which are indicative of critical behavior in 2D percolation problems. Subsequently, the so called Cardy-Carleson functions are demonstrated to satisfy, in the continuum limit, Cardy's formula for crossing probabilities. This extends the results of S. Smirnov to a non-trivial class of critical 2D percolation systems.

Affiliated with

Also associated with

No associations

Rating

Cardy's Formula for Certain Models of the Bond-Triangular Type does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Cardy's Formula for Certain Models of the Bond-Triangular Type, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Cardy's Formula for Certain Models of the Bond-Triangular Type will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-495324