Self-organized Criticality and Absorbing States: Lessons from the Ising Model

Abstract

We investigate a suggested path to self-organized criticality. Originally, this path was devised to "generate criticality" in systems displaying an absorbing-state phase transition, but closer examination of the mechanism reveals that it can be used for any continuous phase transition. We used the Ising model as well as the Manna model to demonstrate how the finite-size scaling exponents depend on the tuning of driving and dissipation rates with system size.Our findings limit the explanatory power of the mechanism to non-universal critical behavior.

arXiv comment5 pages, 2 figures, REVTeX 4

References in corpus (14)

• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Paths to Self-Organized Criticality
• How self-organized criticality works: A unified mean-field picture
• A Complexity View of Rainfall
• Self-organized criticality as an absorbing-state phase transition
• Absorbing-state phase transitions in fixed-energy sandpiles
• Driving, conservation and absorbing states in sandpiles
• Order Parameter and Scaling Fields in Self-Organized Criticality
• Critical behavior of a one-dimensional fixed-energy stochastic sandpile
• Nonequilibrium Phase Transitions in Epidemics and Sandpiles
• Energy constrained sandpile models
• Anisotropy and universality: the Oslo model, the rice pile experiment and the quenched Edwards-Wilkinson equation
• Avalanche Behavior in an Absorbing State Oslo Model
• Disorder-induced phase transition in a one-dimensional model of rice pile

Cited by in corpus (13)

• Critical phenomena in atmospheric precipitation
• 25 Years of Self-Organized Criticality: Concepts and Controversies
• Self-organization without conservation: true or just apparent scale-invariance?
• The approach to criticality in sandpiles
• Persistent dynamic correlations in self-organized critical systems away from their critical point
• Criticality and self-organization in branching processes: application to natural hazards
• Sticky grains do not change the universality class of isotropic sandpiles
• Comment on ``Self-organized criticality and absorbing states: Lessons from the Ising model"
• Equivalence of conditional and external field ensembles in absorbing state phase transitions
• Macroscopic control parameter for avalanche models for bursty transport
• Reply to "Comment on `Self-organized Criticality and Absorbing States: Lessons from the Ising Model'"
• Universality under conditions of self-tuning
• Critical Density of the Abelian Manna Model via a Multi-type Branching Process