Crossover component in non critical dissipative sandpile models

Abstract

The effect of bulk dissipation on non critical sandpile models is studied using both multifractal and finite size scaling analyses. We show numerically that the local limited (LL) model exhibits a crossover from multifractal to self-similar behavior as the control parameters $h_{ext}$ and $ε$ turn towards their critical values, i.e. $h_{ext} \to 0^+ $ and $ε\to ε_c$. The critical exponents are not universal and exhibit a continuous variation with $ε$. On the other hand, the finite size effects for the local unlimited (LU), non local limited (NLL), and non local unlimited (NLU) models are well described by the multifractal analysis for all values of dissipation rate $ε$. The space-time avalanche structure is studied in order to give a deeper understanding of the finite size effects and the origin of the crossover behavior. This result is confirmed by the calculation of the susceptibility.