SELF-ORGANIZED CRITICALITY CAN EMERGE EVEN IF THE RANGE OF INTERACTIONS IS INFINITE

We have investigated a model of tree growth in order to show that self -organized criticality (SOC) can emerge even if perturbations due to l ong-range interactions are propagating throughout the whole system. Th e interaction potential is assumed to be a power d(-alpha) of the dist ance d measured along the tree between branch extremities. A transitio n occurs for alpha(c)=1 according to simulation results between SOC (a lpha>alpha(c)) and non-SOC (alpha<alpha(c)) regimes. A theoretical tre atment supports the idea that the transition occurs when the exponent a is equivalent to the fractal dimension D-f(S) of the backbone (skele ton) of the tree.