Explicit characterization of the identity configuration in an Abelian Sandpile Model

Details Explicit characterization of the identity configuration in an Abelian Sandpile Model Explicit characterization of the identity configuration in an Abelian Sandpile Model

2008-09-19

arxiv.org/abs/0809.3416v2

J.Phys.A41:495003,2008

Physics

Condensed Matter

Statistical Mechanics

11 pages, 8 figures

Scientific paper

10.1088/1751-8113/41/49/495003

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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