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Abstract
Effects of distant-neighbor interactions in the site percolation problem are studied in terms of the renormalization-group transformation in square, triangular, simple cubic, body-centered cubic and face-centred cubic lattices. For the square lattice we consider up to the second-, fifth- and eighth-neighbor interactions for the scale factor of the transformations b=2, 3 and 4, respectively. For other lattices the first-, second- and third-neighbor interactions are taken into account. The results for critical probabilities pc, although not for correlation length exponents νp, agree fairly well with the known data. For the square lattice with the first-neighbor interactions and with the first- and second-neighbor interactions, we obtain νp=1.635, 1.625 and 1.607 for b=2, 3 and 4, respectively, which excellently agree with each other for each value of b. In addition, νp for the simple cubic lattice with up to the third-neighbor interactions coincide closely, within 0.6% precision, with each other.
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