Absorbing states and elastic interfaces in random media: two equivalent descriptions of self-organized criticality

TL;DR

This paper demonstrates the equivalence between depinning transitions of elastic interfaces and absorbing phase transitions in describing self-organized criticality in sandpile models, unifying two previously separate frameworks.

Contribution

It establishes a theoretical equivalence between two descriptions of sandpile criticality, resolving a long-standing puzzle in non-equilibrium universality classes.

Findings

Depinning transitions and absorbing phase transitions are equivalent descriptions.

Local roughening properties differ despite the equivalence.

Implications for experiments and future research are discussed.

Abstract

We elucidate a long-standing puzzle about the non-equilibrium universality classes describing self-organized criticality in sandpile models. We show that depinning transitions of linear interfaces in random media and absorbing phase transitions (with a conserved non-diffusive field) are two equivalent languages to describe sandpile criticality. This is so despite the fact that local roughening properties can be radically different in the two pictures, as explained here. Experimental implications of our work as well as promising paths for future theoretical investigations are also discussed.