SELF-ORGANIZED BRANCHING-PROCESSES - AVALANCHE MODELS WITH DISSIPATION

We explore, in the mean-field approximation, robustness with respect t o dissipation of self-organized criticality in sandpile models. To thi s end, we generalize a recently introduced self-organized branching pr ocess, and show that the model self-organizes not into a critical stat e but rather into a subcritical state: when dissipation is present, th e dynamical fixed point does not coincide with the critical point. Thu s the level of dissipation acts as a relevant parameter in the renorma lization-group sense. We study the model numerically and compute analy tically the critical exponents for the avalanche size and lifetime dis tributions and the scaling exponents for the corresponding cutoffs.