Boundary conditions and defect lines in the Abelian sandpile model.
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.
Jeng
M
M
Department of Physics, Southern Illinois University Edwardsville, Edwardsville, Illinois 62025, USA. mjeng@siue.edu