Factorization of correlations in two-dimensional percolation on the plane and torus

Details Factorization of correlations in two-dimensional percolation on the plane and torus Factorization of correlations in two-dimensional percolation on the plane and torus

2010-11-04

arxiv.org/abs/1011.1101v2

J.Phys.A44:065002,2011

Physics

Condensed Matter

Disordered Systems and Neural Networks

Small corrections (final version). In press, J. Phys. A

Scientific paper

10.1088/1751-8113/44/6/065002

Recently, Delfino and Viti have examined the factorization of the three-point density correlation function P_3 at the percolation point in terms of the two-point density correlation functions P_2. According to conformal invariance, this factorization is exact on the infinite plane, such that the ratio R(z_1, z_2, z_3) = P_3(z_1, z_2, z_3) [P_2(z_1, z_2) P_2(z_1, z_3) P_2(z_2, z_3)]^{1/2} is not only universal but also a constant, independent of the z_i, and in fact an operator product expansion (OPE) coefficient. Delfino and Viti analytically calculate its value (1.022013...) for percolation, in agreement with the numerical value 1.022 found previously in a study of R on the conformally equivalent cylinder. In this paper we confirm the factorization on the plane numerically using periodic lattices (tori) of very large size, which locally approximate a plane. We also investigate the general behavior of R on the torus, and find a minimum value of R approx. 1.0132 when the three points are maximally separated. In addition, we present a simplified expression for R on the plane as a function of the SLE parameter kappa.

Affiliated with

Also associated with

No associations

Rating

Factorization of correlations in two-dimensional percolation on the plane and torus 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 correlations in two-dimensional percolation on the plane and torus, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Factorization of correlations in two-dimensional percolation on the plane and torus will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-145569