Mean Field Behaviour in a Local Low-Dimensional Model

Details Mean Field Behaviour in a Local Low-Dimensional Model Mean Field Behaviour in a Local Low-Dimensional Model

1994-09-16

arxiv.org/abs/cond-mat/9409067v1

Physics

Condensed Matter

11 pages, NLATEX

Scientific paper

10.1209/0295-5075/30/6/001

We point out a new mechanism which can lead to mean field type behaviour in nonequilibrium critical phenomena. We demonstrate this mechanism on a two-dimensional model which can be understood as a stochastic and non-conservative version of the abelian sandpile model of Bak {\it et al.} ~\cite{bak}. This model has a second order phase transition whose critical behaviour seems at least partly described by the mean field approximation for percolation, in spite of the low dimension and the fact that all interactions are of short range. Furthermore, the approximation obtained by replacing the lattice by a Bethe tree is very precise in the entire range of the control parameter.

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