Sandpiles with height restrictions.
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.
Dickman
Ronald
R
Departamento de Física, ICEx, Universidade Federal de Minas Gerais, Caixa Postal 702, 30161-970 Belo Horizonte, MG, Brazil. dickman@fisica.ufmg.br
Tomé
Tânia
T
de Oliveira
Mário J
MJ