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

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 $\nu \approx 1$.

7 pages, 9 figures

References in corpus (3)

• Percolation in Hierarchical Scale-Free Nets
• Small-World Bonds and Patchy Percolation on the Hanoi Network
• Bounds of percolation thresholds in the enhanced binary tree