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On surface properties of two-dimensional percolation clusters

S L A de Queiroz
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Abstract

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, $η_s = 0.6664 \pm 0.0008$, consistent with the analytical value $η_s = 2/3$. 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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S L A de Queiroz. 1995-06-01. On surface properties of two-dimensional percolation clusters. https://doi.org/10.1088/0305-4470%2F28%2F13%2F002

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