Sandpiles and absorbing-state phase transitions: recent results and open problems

Details Sandpiles and absorbing-state phase transitions: recent results and open problems Sandpiles and absorbing-state phase transitions: recent results and open problems

2000-11-27

arxiv.org/abs/cond-mat/0011447v1

Physics

Condensed Matter

10 pages. Latex (aipproc.sty). To appear in the Proceedings of the 6th Granada Seminar on Computational Physics, Ed. J. Marro

Scientific paper

10.1063/1.1386824

We review some recent results on the relations between sandpiles and a class of absorbing state phase transitions. We use the concept of fixed energy sandpiles (FES), in which external driving and dissipation are absent. FES are shown to exhibit an absorbing state transition with critical properties coinciding with those of the corresponding sandpile model. We propose a set of Langevin equations capturing the relevant features of this transition. These equations characterize the universality class of systems with an infinite number of absorbing states and a static conserved field coupled to the order parameter. Different models in this class are identified, and strong evidence is presented showing that the Manna sandpile, as well as some other stochastic sandpiles, belong in this universality class. Finally some open problems and questions are discussed.

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