Münster 1999 – wissenschaftliches Programm
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DY: Dynamik und Statistische Physik
DY 20: POSTER I
DY 20.33: Poster
Dienstag, 23. März 1999, 09:30–13:00, F
Green functions, spanning trees and avalanches in the Abelian sandpile model — •S. Lübeck1, D. V. Ktitarev1,2, P. Grassberger2, and V. B. Priezzhev3 — 1Theoretische Physik, Gerhard-Mercator-Universität, 47048 Duisburg — 2Höchstleistungsrechenzentrum, Forschungszentrum Jülich, 52425 Jülich — 3Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980, Russia
We study the Abelian Bak-Tang-Wiesenfeld sandpile model on a hypercubic lattice for dimensions D=2,3,4. We investigate the probability distributions for avalanches which start at the boundary or at a given distance from the boundary. Using the formalism of Green functions for waves of topplings it is possible to calculate analytically the critical exponents for avalanches neglecting multiple toppling events. Numerical investigations confirm these theoretical predictions. The correspondence of the spanning-tree representation of the avalanches in the Bak-Tang-Wiesenfeld model and the loop-erased random walks allows us to estimate the dynamical exponent of the sandpile model and reveals that the upper critical dimension of the Bak-Tang-Wiesenfeld model is four. For D=2 we confirm recent claims that standard finite size scaling is violated, but our results disagree with these claims in details.