Crossover component in non critical dissipative sandpile models

TL;DR

This paper investigates how bulk dissipation influences non-critical sandpile models, revealing a crossover from multifractal to self-similar behavior near critical parameters and analyzing the effects on various models through multifractal and finite size scaling methods.

Contribution

It demonstrates the crossover behavior in non-critical sandpile models and characterizes the effects of dissipation on their scaling properties and universality.

Findings

Crossover from multifractal to self-similar behavior as parameters approach critical values.

Critical exponents vary continuously with dissipation rate.

Finite size effects are well described by multifractal analysis across 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 $\epsilon$ turn towards their critical values, i.e. $h_{ext} \to 0^+ $ and $\epsilon \to \epsilon_c$. The critical exponents are not universal and exhibit a continuous variation with $\epsilon$. 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 $\epsilon$. 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.