@article{eprints1871,
           title = {Mean-field behavior of the sandpile model below the upper critical dimension},
            year = {1998},
          author = {Alessandro Chessa and Enzo Marinari and Alessandro Vespignani and Stefano Zapperi},
         journal = {Physical Review E},
          volume = {57},
           pages = {R6241--R6244},
       publisher = {American Physical Society},
           month = {June},
        keywords = {PACS: 64.60.Lx, 05.40.+j, 05.70.Ln
},
        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{\ensuremath{<}}{\texttt{\char126}}d{\ensuremath{<}}{\texttt{\char126}}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{\ensuremath{>}}{\texttt{\char126}}5. Using the relations among the dissipation rate {\ensuremath{\epsilon}} 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.},
             url = {http://eprints.imtlucca.it/1871/}
}