Explicit characterization of the identity configuration in an Abelian Sandpile Model

Caracciolo, Sergio; Paoletti, Guglielmo; Sportiello, Andrea

Explicit characterization of the identity configuration in an Abelian Sandpile Model

Authors

Caracciolo, Sergio

Paoletti, Guglielmo

Sportiello, Andrea

Description

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.
11 pages, 8 figures