Recursive percolation

Xuan-Wen Liu, Youjin Deng, Jesper Lykke Jacobsen
2015 Physical Review E  
We introduce a simple lattice model in which percolation is constructed on top of critical percolation clusters, and show that it can be repeated recursively any number n of generations. In two dimensions, we determine the percolation thresholds up to n=5. The corresponding critical clusters become more and more compact as n increases, and define universal scaling functions of the standard two-dimensional form and critical exponents that are distinct for any n. This family of exponents differs
more » ... rom any previously known universality class, and cannot be accommodated by existing analytical methods. We confirm that recursive percolation is well defined also in three dimensions.
doi:10.1103/physreve.92.010103 pmid:26274102 fatcat:zdiuzsb3ybasfaui25nusngsce