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arXiv · 1105.1009

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

Seung Ki Baek·Petter Minnhagen
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Abstract

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 $ν\approx 1$.

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Seung Ki Baek, Petter Minnhagen. 2011-05-05. Hierarchical renormalization-group study on the planar bond-percolation problem. https://doi.org/10.1088/0031-8949%2F83%2F05%2F055601

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