A Transfer Matrix for the Backbone Exponent of Two-Dimensional Percolation
Statistical Mechanics
2009-11-07 v2
Abstract
Rephrasing the backbone of two-dimensional percolation as a monochromatic path crossing problem, we investigate the latter by a transfer matrix approach. Conformal invariance links the backbone dimension D_b to the highest eigenvalue of the transfer matrix T, and we obtain the result D_b=1.6431 \pm 0.0006. For a strip of width L, T is roughly of size 2^{3^L}, but we manage to reduce it to \sim L!. We find that the value of D_b is stable with respect to inclusion of additional ``blobs'' tangent to the backbone in a finite number of points.
Cite
@article{arxiv.cond-mat/0111374,
title = {A Transfer Matrix for the Backbone Exponent of Two-Dimensional Percolation},
author = {J. L. Jacobsen and P. Zinn-Justin},
journal= {arXiv preprint arXiv:cond-mat/0111374},
year = {2009}
}
Comments
19 pages