Expansion Around the Mean-Field Solution of the Bak-Sneppen Model

Details Expansion Around the Mean-Field Solution of the Bak-Sneppen Model Expansion Around the Mean-Field Solution of the Bak-Sneppen Model

1997-10-15

arxiv.org/abs/cond-mat/9710152v1

Phys. Rev. Lett. 80, 1457 (1998).

Physics

Condensed Matter

Statistical Mechanics

5 pages, 2 ps-figures icluded

Scientific paper

10.1103/PhysRevLett.80.1457

We study a recently proposed equation for the avalanche distribution in the Bak-Sneppen model. We demonstrate that this equation indirectly relates $\tau$,the exponent for the power law distribution of avalanche sizes, to $D$, the fractal dimension of an avalanche cluster.We compute this relation numerically and approximate it analytically up to the second order of expansion around the mean field exponents. Our results are consistent with Monte Carlo simulations of Bak-Sneppen model in one and two dimensions.

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