Eulerian Walkers as a model of Self-Organised Criticality

Details Eulerian Walkers as a model of Self-Organised Criticality Eulerian Walkers as a model of Self-Organised Criticality

1996-11-04

arxiv.org/abs/cond-mat/9611019v1

Phys. Rev. Lett. 77 (1996) 5079.

Physics

Condensed Matter

Statistical Mechanics

4 pages, RevTex, 4 figures

Scientific paper

10.1103/PhysRevLett.77.5079

We propose a new model of self-organized criticality. A particle is dropped at random on a lattice and moves along directions specified by arrows at each site. As it moves, it changes the direction of the arrows according to fixed rules. On closed graphs these walks generate Euler circuits. On open graphs, the particle eventually leaves the system, and a new particle is then added. The operators corresponding to particle addition generate an abelian group, same as the group for the Abelian Sandpile model on the graph. We determine the critical steady state and some critical exponents exactly, using this equivalence.

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