| Issue |
J. Phys. I France
Volume 3, Number 8, August 1993
|
|
|---|---|---|
| Page(s) | 1729 - 1740 | |
| DOI | https://doi.org/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. PriezzhevLaboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, 141980, Russia
(Received 22 March 1993, accepted 25 April 1993)
Abstract
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
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,
, 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.
© Les Editions de Physique 1993