Analytical approach to directed sandpile models on the Apollonian network

Details Analytical approach to directed sandpile models on the Apollonian network Analytical approach to directed sandpile models on the Apollonian network

2007-01-29

arxiv.org/abs/cond-mat/0701723v2

Phys. Rev. E 76, 026111 (2007)

Physics

Condensed Matter

Statistical Mechanics

7 pages in two-column format, 10 illustrations, 5 figures

Scientific paper

10.1103/PhysRevE.76.026111

We investigate a set of directed sandpile models on the Apollonian network, which are inspired on the work by Dhar and Ramaswamy (PRL \textbf{63}, 1659 (1989)) for Euclidian lattices. They are characterized by a single parameter $q$, that restricts the number of neighbors receiving grains from a toppling node. Due to the geometry of the network, two and three point correlation functions are amenable to exact treatment, leading to analytical results for the avalanche distributions in the limit of an infinite system, for $q=1,2$. The exact recurrence expressions for the correlation functions are numerically iterated to obtain results for finite size systems, when larger values of $q$ are considered. Finally, a detailed description of the local flux properties is provided by a multifractal scaling analysis.

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