We investigate bond percolation on the nonplanar Hanoi network (HN-NP), which was studied previously. We calculate the fractal exponent of a subgraph of the HN-NP, which gives a lower bound for the fractal exponent of the original graph. This lower bound leads to the conclusion that the original system does not have a nonpercolating phase, where only finite-size clusters exist for p>0, or equivalently, that the system exhibits either the critical phase, where infinitely many infinite clusters exist, or the percolating phase, where a unique giant component exists. Monte Carlo simulations support our conjecture.
|Journal||Physical Review E - Statistical, Nonlinear, and Soft Matter Physics|
|Publication status||Published - 2013 Mar 18|
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics