Boundary effects in a two-dimensional Abelian sandpile

We study boundary and finite-size effects in the Abelian sandpile model due to Bak, Tang and Wiesenfeld. In the case of half-plane geometry, the probability $mathcal{P}_1(r)$ of a unit height at the boundary, and at a distance r inside the sample is found for open and closed boundary conditions. The leading asymptotic form of the correlation functions for the unit heights, $mathcal{P}_{11}(r)$, in the strip and half-plane geometries is obtained for different boundary conditions too. Our results confirm the hypothesis that the unit height behaves like the local energy operator in the zero-component limit of the Potts model