Abstract
We introduce new avalanche models on the d-dimensional hyper-cubic lattices which show the self-organized criticality (SOC). They are generalization of the two-state exclusive diffusion model introduced in our previous paper and called the n-state exclusive diffusion models (1≤ n≤ 2d). If n=2d, this model is the sandpile model of Bak, Tang and Wiesenfeld. By Monte Carlo simulations, we evaluated the height distributions of particles and the avalanche exponents for d=2,3, and 4. Numerical results imply that the n-state exclusive diffusion models belong to the same universality class for each d, if 2≤ n≤ 2d. We apply the mean-field approximation and evaluate the height distributions of particles in the SOC states. It is shown that the mean-field theory by Tang and Bak is the d→ ∞ limit of our mean-field approximation.
