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

J. L. Jacobsen·P. Zinn-Justin
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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.

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J. L. Jacobsen, P. Zinn-Justin. 2002-01-30. A Transfer Matrix for the Backbone Exponent of Two-Dimensional Percolation. https://doi.org/10.1088/0305-4470%2F35%2F9%2F304

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