On surface properties of two-dimensional percolation clusters

Details On surface properties of two-dimensional percolation clusters On surface properties of two-dimensional percolation clusters

1995-06-01

arxiv.org/abs/cond-mat/9506005v1

Journal of Physics A 28, L363 (1995)

Physics

Condensed Matter

8 pages, LaTeX with Institute of Physics macros, to appear in Journal of Physics A

Scientific paper

10.1088/0305-4470/28/13/002

The two-dimensional site percolation problem is studied by transfer-matrix methods on finite-width strips with free boundary conditions. The relationship between correlation-length amplitudes and critical indices, predicted by conformal invariance, allows a very precise determination of the surface decay-of-correlations exponent, $\eta_s = 0.6664 \pm 0.0008$, consistent with the analytical value $\eta_s = 2/3$. It is found that a special transition does not occur in the case, corroborating earlier series results. At the ordinary transition, numerical estimates are consistent with the exact value $y_s = -1$ for the irrelevant exponent.

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