1212.5545 (Takehisa Hasegawa et al.)

Absence of the non-percolating phase for percolation on the non-planar
Hanoi network    [PDF]

Takehisa Hasegawa, Tomoaki Nogawa

We investigate bond percolation on the non-planar Hanoi network (HN-NP), which was studied in [Boettcher et al. Phys. Rev. E 80 (2009) 041115]. 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 non-percolating phase, where only finite size clusters exist, for p>0, or equivalently, that the system exhibits either in 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.

View original: http://arxiv.org/abs/1212.5545