Abstract
The effects of surfaces on percolation are investigated near the bulk percolation threshold ind=6−ε dimensions. Using field-theoretic methods, this is done within the framework of a semi-infinite continuousq-state Potts model withq→1. Renormalization-group equations are obtained which imply that the usual scaling laws for surface and bulk exponents are valid to all orders in ε, and the surface exponents at the ordinary and special transition are computed to order ε. Our result for β ord1 is in conformity with the one by Carton.
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Diehl, H.W., Lam, P.M. Semi-infinite Potts model and percolation at surfaces. Z. Physik B - Condensed Matter 74, 395–401 (1989). https://doi.org/10.1007/BF01307889
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DOI: https://doi.org/10.1007/BF01307889