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Sandpiles with height restrictions

Ronald Dickman·Tania Tome·Mario J. de Oliveira
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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.

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Ronald Dickman, Tania Tome, Mario J. de Oliveira. 2002-03-27. Sandpiles with height restrictions. https://doi.org/10.1103/physreve.66.016111

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