• Rapid Communication

Mean-field behavior of the sandpile model below the upper critical dimension

Alessandro Chessa, Enzo Marinari, Alessandro Vespignani, and Stefano Zapperi
Phys. Rev. E 57, R6241(R) – Published 1 June 1998
PDFExport Citation

Abstract

We present results of large scale numerical simulations of the Bak, Tang, and Wiesenfeld [Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A 38, 364 (1988)] sandpile model. We analyze the critical behavior of the model in Euclidean dimensions 2<~d<~6. We consider a dissipative generalization of the model and study the avalanche size and duration distributions for different values of the lattice size and dissipation. We find that the scaling exponents in d=4 significantly differ from mean-field predictions, thus suggesting an upper critical dimension dc>~5. Using the relations among the dissipation rate ε and the finite lattice size L, we find that a subset of the exponents displays mean-field values below the upper critical dimensions. This behavior is explained in terms of conservation laws.

  • Received 18 February 1998

DOI:https://doi.org/10.1103/PhysRevE.57.R6241

©1998 American Physical Society

Authors & Affiliations

Alessandro Chessa1,2, Enzo Marinari1,3, Alessandro Vespignani4, and Stefano Zapperi5

  • 1Dipartimento di Fisica, Universitá di Cagliari, Via Ospedale 72, 09124 Cagliari, Italy
  • 2Istituto Nazionale di Fisica della Materia (INFM), Sezione di Cagliari, 09124 Cagliari, Italy
  • 3Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Cagliari, 09124 Cagliari, Italy
  • 4The Abdus Salam International Centre for Theoretical Physics (ICTP), P.O. Box 586, 34100 Trieste, Italy
  • 5Center for Polymer Studies and Department of Physics Boston University, Boston, Massachusetts 02215

References (Subscription Required)

Click to Expand
Issue

Vol. 57, Iss. 6 — June 1998

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×