Exact solution of the one-dimensional deterministic Fixed-Energy Sandpile

Abstract

In reason of the strongly non-ergodic dynamical behavior, universality properties of deterministic Fixed-Energy Sandpiles are still an open and debated issue. We investigate the one-dimensional model, whose microscopical dynamics can be solved exactly, and provide a deeper understanding of the origin of the non-ergodicity. By means of exact arguments, we prove the occurrence of orbits of well-defined periods and their dependence on the conserved energy density. Further statistical estimates of the size of the attraction's basins of the different periodic orbits lead to a complete characterization of the activity vs. energy density phase diagram in the limit of large system's size.

4 pages, accepted for publication in Phys. Rev. Lett

References in corpus (15)

• Universal scaling behavior of non-equilibrium phase transitions
• The universality class of absorbing phase transitions with a conserved field
• Self-organized criticality as an absorbing-state phase transition
• Transport in Sand Piles, Interface Depinning, and Earthquake Models
• Absorbing-state phase transitions in fixed-energy sandpiles
• Driving, conservation and absorbing states in sandpiles
• Multifractal scaling in the Bak-Tang-Wiesenfeld Sandpile and edge events
• Universality in sandpiles
• Rare events and breakdown of simple scaling in the Abelian sandpile
• Scaling of waves in the Bak-Tang-Wiesenfeld sandpile model
• Avalanches and the Renormalization Group for Pinned Charge-Density Waves
• Algebraic Aspects of Abelian Sandpile Models
• Critical behavior of a one-dimensional fixed-energy stochastic sandpile
• Universality Classes in Isotropic, Abelian and non-Abelian, Sandpile Models
• Short period attractors and non-ergodic behavior in the deterministic fixed energy sandpile model

Cited by in corpus (7)

• The approach to criticality in sandpiles
• Self-organized quantization and oscillations on continuous fixed-energy sandpiles
• Parallel Chip-Firing on the Complete Graph: Devil's Staircase and Poincare Rotation Number
• Dynamical Invariants in the Deterministic Fixed-Energy Sandpile
• A Variation on Chip-Firing: the diffusion game
• Abelian networks IV. Dynamics of nonhalting networks
• Emergence of oscillations in fixed energy sandpile models on complex networks