The Upper Critical Dimension of the Abelian Sandpile Model
| dc.creator | Priezzhev, V. B. | |
| dc.date | 1999-04-04 | |
| dc.date.accessioned | 2026-07-07T03:13:11Z | |
| dc.date.available | 2026-07-07T03:13:11Z | |
| dc.description | The existing estimation of the upper critical dimension of the Abelian Sandpile Model is based on a qualitative consideration of avalanches as self-avoiding branching processes. We find an exact representation of an avalanche as a sequence of spanning sub-trees of two-component spanning trees. Using equivalence between chemical paths on the spanning tree and loop-erased random walks, we reduce the problem to determination of the fractal dimension of spanning sub-trees. Then, the upper critical dimension $d_u=4$ follows from Lawler's theorems for intersection probabilities of random walks and loop-erased random walks. | |
| dc.description | 16 pages | |
| dc.identifier | https://arxiv.org/abs/cond-mat/9904054 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/9904054 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/29199 | |
| dc.subject | Statistical Mechanics | |
| dc.title | The Upper Critical Dimension of the Abelian Sandpile Model | |
| dc.type | text |