MEAN-FIELD BEHAVIOR IN A LOCAL LOW-DIMENSIONAL MODEL

We point out a new mechanism which can lead to mean-field-type behaviour in non-equilibrium critical phenomena. We demonstrate this mechanism on a two-dimensional model which can be understood as a stochastic and non-conservative version of the Abelian sandpile model of Bak et al. (Phys. Rev. Lett., 59 (1987) 381). This model has a second-order phase transition whose critical behaviour seems at least partly described by the mean-field approximation for percolation, in spite of the low dimension and the fact that ail interactions are of short range. Furthermore, the approximation obtained by replacing the lattice by a Bethe tree is very precise in the entire range of the control parameter.