Abstract
The bond percolation on a three-dimensional semi-infinite simple cubic lattice is considered. It is assumed that the probability of a bond being present in the surface layer may be different from the probability of a bond inside the lattice. The mean size of finite clusters is studied. Using the relation between the Potts model and the bond percolation process, and applying the mean-field approximation, analytical formulae for the mean cluster size near the ordinary, surface-bulk, extraordinary and surface second-order phase transitions are obtained. The effect of the surface on the mean cluster size is discussed.
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