Renormalization-Group Transformation for Site Percolation Problem with Distant-Neighbor Interactions

概要

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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 P_c, although not for correlation length exponents ν_p, 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 ν_p=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, ν_p for the simple cubic lattice with up to the third-neighbor interactions coincide closely, within 0. 6% precision, with each other.
理論物理学刊行会の論文
1980-09-25