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.

The abstract of this article has been published in the "Intellectual Archive Bulletin" , May 2012, ISSN 1929-1329.

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hierarchical long-range percolation graph.pdf

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