Explicit characterization of the identity configuration in an Abelian Sandpile Model

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Caracciolo, Sergio
Paoletti, Guglielmo
Sportiello, Andrea
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Abstract
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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.
Comment: 11 pages, 8 figures
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Condensed Matter - Statistical Mechanics, High Energy Physics - Lattice, Mathematical Physics, Nonlinear Sciences - Adaptation and Self-Organizing Systems
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