A Transfer Matrix for the Backbone Exponent of Two-Dimensional Percolation

Details A Transfer Matrix for the Backbone Exponent of Two-Dimensional Percolation A Transfer Matrix for the Backbone Exponent of Two-Dimensional Percolation

2001-11-20

arxiv.org/abs/cond-mat/0111374v2

J. Phys. A 35 (2002), 2131--2144

Physics

Condensed Matter

Statistical Mechanics

19 pages

Scientific paper

10.1088/0305-4470/35/9/304

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.

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