Levy-Nearest-Neighbors Bak-Sneppen Model

Details Levy-Nearest-Neighbors Bak-Sneppen Model Levy-Nearest-Neighbors Bak-Sneppen Model

1999-06-22

arxiv.org/abs/cond-mat/9906337v1

Physics

Condensed Matter

Statistical Mechanics

To appear on Phys. Rev. E, Rapid Communications

Scientific paper

10.1103/PhysRevE.60.R1111

We study a random neighbor version of the Bak-Sneppen model, where "nearest neighbors" are chosen according to a probability distribution decaying as a power-law of the distance from the active site, P(x) \sim |x-x_{ac }|^{-\omega}. All the exponents characterizing the self-organized critical state of this model depend on the exponent \omega. As \omega tends to 1 we recover the usual random nearest neighbor version of the model. The pattern of results obtained for a range of values of \omega is also compatible with the results of simulations of the original BS model in high dimensions. Moreover, our results suggest a critical dimension d_c=6 for the Bak-Sneppen model, in contrast with previous claims.

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