MEAN-FIELD BEHAVIOR OF THE SANDPILE MODEL BELOW THE UPPER CRITICAL DIMENSION

We present results of large scale numerical simulations of the Bak, Ta ng, and Wiesenfeld [Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A 38, 364 (1988)] sandpile model. We analyze the critical behavior of the mo del in Euclidean dimensions 2 less than or equal to d less than or equ al to 6. We consider a dissipative generalization of the model and stu dy the avalanche size and duration distributions for different values of the lattice size and dissipation. We find that the scaling exponent s in d=4 significantly differ from mean-field predictions, thus Sugges ting an upper critical dimension d(c)greater than or equal to 5. Using the relations among the dissipation rate epsilon and the finite latti ce 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.