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Universality Class of One-Dimensional Directed Sandpile Models

Matthew Stapleton·Kim Christensen
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Abstract

A general n-state directed `sandpile' model is introduced. The stationary properties of the n-state model are derived for n < infty, and analytical arguments based on a central limit theorem show that the model belongs to the universality class of the totally asymmetric Oslo model, with a crossover to uncorrelated branching process behavior for small system sizes. Hence, the central limit theorem allows us to identify the existence of a large universality class of one-dimensional directed sandpile models.

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BibTeXRIS

Matthew Stapleton, Kim Christensen. 2005-06-29. Universality Class of One-Dimensional Directed Sandpile Models. https://doi.org/10.1103/physreve.72.066103

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