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Boundary conditions and defect lines in the Abelian sandpile model

Monwhea Jeng
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Abstract

We add a defect line of dissipation, or crack, to the Abelian sandpile model. We find that the defect line renormalizes to separate the two-dimensional plane into two half planes with open boundary conditions. We also show that varying the amount of dissipation at a boundary of the Abelian sandpile model does not affect the universality class of the boundary condition. We demonstrate that a universal coefficient associated with height probabilities near the defect can be used to classify boundary conditions.

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Monwhea Jeng. 2004-05-25. Boundary conditions and defect lines in the Abelian sandpile model. https://doi.org/10.1103/physreve.69.051302

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