Infinite Hierarchy of Exact Equations in the Bak-Sneppen Model

Details Infinite Hierarchy of Exact Equations in the Bak-Sneppen Model Infinite Hierarchy of Exact Equations in the Bak-Sneppen Model

1996-01-18

arxiv.org/abs/adap-org/9601003v1

Phys. Rev. Lett. 77, 1182 (1996)

Physics

Condensed Matter

Submitted to PRL, 4 two-column pages (revtex), 1 ps figure included with epsf, g-zipped, uuencoded

Scientific paper

10.1103/PhysRevLett.77.1182

We derive an infinite hierarchy of exact equations for the Bak-Sneppen model in arbitrary dimensions. These equations relate different moments of temporal duration and spatial size of avalanches. We prove that the exponents of the BS model are the same above and below the critical point and express the universal amplitude ratio of the avalanche spatial size in terms of the critical exponents. The equations uniquely determine the shape of the scaling function of the avalanche distribution. It is suggested that in the BS model there is only one independent critical exponent.

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