Explicit characterization of the identity configuration in an Abelian Sandpile Model

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.

arXiv comment11 pages, 8 figures

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Cited by in corpus (14)

• Holographic applications of logarithmic conformal field theories
• On the Sandpile group of the cone of a graph
• Pattern formation in growing sandpiles
• Logarithmic conformal invariance in the Abelian sandpile model
• Multiple and inverse topplings in the Abelian Sandpile Model
• Pattern Formation in Growing Sandpiles with Multiple Sources or Sinks
• Harmonic dynamics of the Abelian sandpile
• Conservation laws for strings in the Abelian Sandpile Model
• Pattern formation in fast-growing sandpiles
• A sandpile model for proportionate growth
• Effect of Noise on Patterns Formed by Growing Sandpiles
• Sandpile models in the large
• Factorization in the multirefined tangent method
• Compatible Recurrent Identities of the Sandpile Group and Maximal Stable Configurations