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.

Explicit characterization of the identity configuration in an Abelian sandpile model / S. Caracciolo, G. Paoletti, A. Sportiello. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL. - ISSN 1751-8113. - 41:49(2008 Oct 29), p. 495003.495003.

Explicit characterization of the identity configuration in an Abelian sandpile model

S. Caracciolo
Primo
;
A. Sportiello
Ultimo
2008

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.
Settore FIS/02 - Fisica Teorica, Modelli e Metodi Matematici
29-ott-2008
http://www.iop.org/EJ/abstract/1751-8121/41/49/495003/
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/52518
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