On surface properties of two-dimensional percolation clusters

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, ${\eta }_s=0.6664\pm 0.0008$, 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.

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

References in corpus (1)

• Transfer-matrix scaling from disorder-averaged correlation lengths for diluted Ising systems

Cited by in corpus (4)

• The raise and peel model of a fluctuating interface
• Surface crossover exponent for branched polymers in two dimensions
• Percolation and Conduction in Restricted Geometries
• Connectivity-dependent properties of diluted sytems in a transfer-matrix description