Bak-Sneppen model near zero dimension

Details Bak-Sneppen model near zero dimension Bak-Sneppen model near zero dimension

2000-03-15

arxiv.org/abs/cond-mat/0003265v2

Phys. Rev. E 62, 295 (2000)

Physics

Condensed Matter

Statistical Mechanics

4 pages revtex (twocolumn, epsfig), 1 figure. Submitted to Phys. Rev. E, Rapid Comm

Scientific paper

10.1103/PhysRevE.62.295

We consider the Bak--Sneppen model near zero dimension where the avalanche exponent $\tau$ is close to 1 and the exponents $\mu$ and $\sigma$ are close to 0. We demonstrate that $\tau-1=\mu-\sigma=\exp\{-\mu^{-1}-\gamma+...\}$ in this limit, where $\gamma$ is the Euler's constant. The avalanche hierarchy equation is rewritten in a form that makes possible to find the relation between the critical exponents $\sigma$ and $\mu$ with high accuracy. We obtain new, more precise, values of the critical exponents for the 1D and 2D Bak-Sneppen model and for the 1D anisotropic Bak-Sneppen model.

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