Abstract
The structure of avalanches in the Abelian sandpile model on a square lattice is analyzed. It is shown that an avalanche can be considered as a sequence of waves of decreasing sizes. Being more simple objects, waves admit a representation in terms of spanning trees covering the lattice sites. The difference in sizes of subsequent waves follows a power law with the exponent simply related to the basic exponent of the sandpile model. Using known exponents for the spanning trees, we derive from scaling arguments and .
- Received 5 July 1995
DOI:https://doi.org/10.1103/PhysRevLett.76.2093
©1996 American Physical Society