Universality Classes in Isotropic, Abelian and non-Abelian, Sandpile Models

Abstract

Universality in isotropic, abelian and non-abelian, sandpile models is examined using extensive numerical simulations. To characterize the critical behavior we employ an extended set of critical exponents, geometric features of the avalanches, as well as scaling functions describing the time evolution of average quantities such as the area and size during the avalanche. Comparing between the abelian Bak-Tang-Wiesenfeld model [P. Bak, C. Tang and K. Wiensenfeld, Phys. Rev. Lett. 59, 381 (1987)], and the non-abelian models introduced by Manna [S. S. Manna, J. Phys. A. 24, L363 (1991)] and Zhang [Y. C. Zhang, Phys. Rev. Lett. 63, 470 (1989)] we find strong indications that each one of these models belongs to a distinct universality class.

18 pages of text, RevTeX, additional 8 figures in 12 PS files

References in corpus (2)

• Universality in Sandpile Models
• Large scale simulations of the Zhang sandpile model

Cited by in corpus (25)

• Power laws and Self-Organized Criticality in Theory and Nature
• 25 Years of Self-Organized Criticality: Concepts and Controversies
• Driving, conservation and absorbing states in sandpiles
• Universality in sandpiles
• Scaling of waves in the Bak-Tang-Wiesenfeld sandpile model
• Field theory of absorbing phase transitions with a non-diffusive conserved field
• Quenched noise and over-active sites in sandpile dynamics
• Universality classes in directed sandpile models
• Exact solution of stochastic directed sandpile model
• Critical behavior and conservation in directed sandpiles
• Exact solution of the one-dimensional deterministic Fixed-Energy Sandpile
• Sandpile models and random walkers on finite lattices
• Characteristics of Deterministic and Stochastic Sandpile Models in a Rotational Sandpile Model
• Dynamically Driven Renormalization Group Applied to Sandpile Models
• Critical properties of a dissipative sandpile model on small world networks
• Steady state of Stochastic Sandpile Models
• Some Properties of Sandpile Models as Prototype of Self-Organized Critical Systems
• Inhomogeneous sandpile model: Crossover from multifractal scaling to finite size scaling
• Self-organized random walks and stochastic sandpile: From linear to branched avalanches
• Modified Renormalization Strategy for Sandpile Models
• Universality of continuous phase transitions on random Voronoi graphs
• Relevance of Abelian Symmetry and Stochasticity in Directed Sandpiles
• Emergence and complexity in theoretical models of self-organized criticality
• Universality classes and crossover behaviors in non-Abelian directed sandpiles
• Emergence of quasi-units in the one dimensional Zhang model