Hierarchical renormalization-group study on the planar bond-percolation problem

Details Hierarchical renormalization-group study on the planar bond-percolation problem Hierarchical renormalization-group study on the planar bond-percolation problem

2011-05-05

arxiv.org/abs/1105.1009v1

Phys. Scr. 83, 055601 (2011)

Physics

Condensed Matter

Statistical Mechanics

7 pages, 9 figures

Scientific paper

10.1088/0031-8949/83/05/055601

For certain hierarchical structures, one can study the percolation problem using the renormalization-group method in a very precise way. We show that the idea can be also applied to two-dimensional planar lattices by regarding them as hierarchical structures. Either a lower bound or an exact critical probability can be obtained with this method and the correlation-length critical exponent is approximately estimated as $\nu \approx 1$.

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