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Percolation at the surface of semi-infinite two-dimensional lattices

1986; American Physical Society; Volume: 33; Issue: 9 Linguagem: Inglês

10.1103/physrevb.33.6446

1095-3795

B. P. Watson,

Random Matrices and Applications

The method of Monte Carlo invariant imbedding is developed to calculate the probability that a site on the surface of a semi-infinite, two-dimensional lattice belongs to the bulk infinite cluster. For the square and triangular lattices, the surface percolation exponent is found to be ${\ensuremath{\beta}}_{1}$=0.398\ifmmode\pm\else\textpm\fi{}0.005. This result is compared with those found indirectly using scaling relations on different surface exponents obtained by other methods.