Energy constrained sandpile models

TL;DR

This paper investigates energy-constrained sandpile models, revealing a new universality class for critical behavior while showing avalanche distributions similar to standard self-organized critical sandpiles.

Contribution

It introduces energy-constrained variants of sandpile models and demonstrates their distinct critical universality class compared to traditional SOC models.

Findings

Models exhibit scale-free behavior at a critical energy E_c

Critical correlations belong to a different universality class than SOC sandpiles

Avalanche size distributions match those of standard SOC sandpiles

Abstract

We study two driven dynamical systems with conserved energy. The two automata contain the basic dynamical rules of the Bak, Tang and Wiesenfeld sandpile model. In addition a global constraint on the energy contained in the lattice is imposed. In the limit of an infinitely slow driving of the system, the conserved energy $E$ becomes the only parameter governing the dynamical behavior of the system. Both models show scale free behavior at a critical value $E_c$ of the fixed energy. The scaling with respect to the relevant scaling field points out that the developing of critical correlations is in a different universality class than self-organized critical sandpiles. Despite this difference, the activity (avalanche) probability distributions appear to coincide with the one of the standard self-organized critical sandpile.