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arXiv · 0809.3416

Explicit characterization of the identity configuration in an Abelian Sandpile Model

Sergio Caracciolo·Guglielmo Paoletti·Andrea Sportiello
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Abstract

Since the work of Creutz, identifying the group identities for the Abelian Sandpile Model (ASM) on a given lattice is a puzzling issue: on rectangular portions of Z^2 complex quasi-self-similar structures arise. We study the ASM on the square lattice, in different geometries, and a variant with directed edges. Cylinders, through their extra symmetry, allow an easy determination of the identity, which is a homogeneous function. The directed variant on square geometry shows a remarkable exact structure, asymptotically self-similar.

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Sergio Caracciolo, Guglielmo Paoletti, Andrea Sportiello. 2008-10-05. Explicit characterization of the identity configuration in an Abelian Sandpile Model. https://doi.org/10.1088/1751-8113/41/49/495003

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