Y Shang. The vertex degree of a hierarchical long-range percolation graph

Natural Sciences / Physics / Mathematical Physics

Submitted on: May 25, 2012, 14:35:26

Description: The use of percolation theory in statistical physics has long been recognized. In this letter, we consider percolation in the hierarchical lattice of order $N$ where the probability of connection between two nodes separated by distance $k$ is of the form $1-e^{-frac{alpha}{beta^k}}$, $alphage0$ and $beta>0$. The vertex degrees of the resulting percolation graph are studied, which are consistent with the phase diagram of this model.