Factorization of percolation density correlation functions for clusters touching the sides of a rectangle

Details Factorization of percolation density correlation functions for clusters touching the sides of a rectangle Factorization of percolation density correlation functions for clusters touching the sides of a rectangle

2008-11-19

arxiv.org/abs/0811.3080v1

J. Stat. Mech. (2009) P02067

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1088/1742-5468/2009/02/P02067

We consider the density at a point z = x + i y of critical percolation clusters that touch the left [P_L(z)], right [P_R(z)], or both [P_{LR}(z)] sides of a rectangular system, with open boundary conditions on the top and bottom. The ratio C(z) = P_{LR}(z) / sqrt[P_L(z) P_R(z) Pi_h], where Pi_h is the probability of horizontal crossing given by Cardy, is a universal function of z and goes to a constant value C_0 = 2^(7/2) 3^(-3/4) pi^(5/2) Gamma(1/3)^(-9/2) = 1.0299268... far from the ends. We observe numerically that C(z) depends upon x but not y for wired b.c., and this result leads to an explicit expression for C(z) via conformal field theory. For the semi-infinite strip we also derive explict expressions for P_L(z), P_R(z), and P_{LR}(z), for both wired and open b.c. Our results enable calculation of the finite-size corrections to the factorization near an isolated anchor point, for the case of clusters anchored at two boundary points. Finally, we present numerical results for a rectangle with periodic b.c. in the horizontal direction, and find that C(z) approaches a constant value C_1 = 1.022.

Affiliated with

Also associated with

No associations

Rating

Factorization of percolation density correlation functions for clusters touching the sides of a rectangle 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 Factorization of percolation density correlation functions for clusters touching the sides of a rectangle, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Factorization of percolation density correlation functions for clusters touching the sides of a rectangle will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-667210