Sandpiles with height restrictions

Abstract

We study stochastic sandpile models with a height restriction in one and two dimensions. A site can topple if it has a height of two, as in Manna's model, but, in contrast to previously studied sandpiles, here the height (or number of particles per site), cannot exceed two. This yields a considerable simplification over the unrestricted case, in which the number of states per site is unbounded. Two toppling rules are considered: in one, the particles are redistributed independently, while the other involves some cooperativity. We study the fixed-energy system (no input or loss of particles) using cluster approximations and extensive simulations, and find that it exhibits a continuous phase transition to an absorbing state at a critical value zeta_c of the particle density. The critical exponents agree with those of the unrestricted Manna sandpile.

arXiv comment10 pages, 14 figures

References in corpus (15)

• Paths to Self-Organized Criticality
• The abelian sandpile and related models
• How self-organized criticality works: A unified mean-field picture
• The universality class of absorbing phase transitions with a conserved field
• Self-organized criticality as an absorbing-state phase transition
• Avalanche and spreading exponents in systems with absorbing states
• Absorbing-state phase transitions in fixed-energy sandpiles
• Driving, conservation and absorbing states in sandpiles
• Order Parameter and Scaling Fields in Self-Organized Criticality
• Moment ratios for absorbing-state phase transitions
• Critical behavior of a one-dimensional fixed-energy stochastic sandpile
• Nonequilibrium Phase Transitions in Epidemics and Sandpiles
• Energy constrained sandpile models
• Pair contact process with a particle source
• The Pair Contact Process in Two Dimensions

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