https://doi.org/10.1007/s100510070048
Anomalous scaling in the Zhang model
1
Dept. de Física Fonamental, Facultat de
Física, Universitat de Barcelona,
Av. Diagonal 647, 08028 Barcelona, Spain
2
The Abdus Salam International Centre for Theoretical Physics
(ICTP), PO Box 586, 34100 Trieste,
Italy
Received:
8
August
2000
Revised:
4
October
2000
Published online: 15 November 2000
We apply the moment analysis technique to analyze large scale simulations of the Zhang sandpile model. We find that this model shows different scaling behavior depending on the update mechanism used. With the standard parallel updating, the Zhang model violates the finite-size scaling hypothesis, and it also appears to be incompatible with the more general multifractal scaling form. This makes impossible its affiliation to any one of the known universality classes of sandpile models. With sequential updating, it shows scaling for the size and area distribution. The introduction of stochasticity into the toppling rules of the parallel Zhang model leads to a scaling behavior compatible with the Manna universality class.
PACS: 05.70.Ln – Nonequilibrium and irreversible thermodynamics / 05.65.+b – Self-organized systems
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000
