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 long-range interactions are propagating throughout the whole system. The interaction potential is assumed to be a power d(-alpha) of the distance d measured along the tree between branch extremities. A transition occurs for alpha(c)=1 according to simulation results between SOC (alpha>alpha(c) and non-SOC (alpha<alpha(c)) regimes. A theoretical treatment supports the idea that the transition occurs when the exponent a is equivalent to the fractal dimension D-f(S) of the backbone (skeleton) of the tree.