Criticality in driven cellular automata with defects

TL;DR

This paper investigates how quenched random defects affect the critical behavior of driven cellular automata, revealing self-organization into critical states under conservative dynamics and subcritical states with nonconservative defects.

Contribution

It introduces three models of driven sandpile automata with defects and analyzes their criticality and phase transitions, highlighting nonuniversal exponents and defect-mediated transitions.

Findings

Models self-organize into critical states with conservative defects.

Nonconservative defects lead to subcritical asymptotic states.

Nonuniversal exponents depend on defect concentration.

Abstract

We study three models of driven sandpile-type automata in the presence of quenched random defects. When the dynamics is conservative, all these models, termed the random sites (A), random bonds (B), and random slopes (C), self-organize into a critical state. For Model C the concentration-dependent exponents are nonuniversal. In the case of nonconservative defects, the asymptotic state is subcritical. Possible defect-mediated nonequilibrium phase transitions are also discussed.