J. Phys. I France
Volume 3, Numéro 8, August 1993
Page(s) 1729 - 1740
DOI: 10.1051/jp1:1993212
J. Phys. I France 3 (1993) 1729-1740

Boundary effects in a two-dimensional Abelian sandpile

J. G. Brankov, E. V. Ivashkevich and V. B. Priezzhev

Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, 141980, Russia

(Received 22 March 1993, accepted 25 April 1993)

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.

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