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

Matteo Marsili; Paolo De Los Rios; Sergei Maslov

doi:10.1103/PhysRevLett.80.1457

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

Statistical Mechanics 2009-10-30 v1 Soft Condensed Matter

Authors: Matteo Marsili , Paolo De Los Rios , Sergei Maslov

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Abstract

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.

Keywords

Bak-Sneppen model avalanche distribution mean-field expansion fractal dimension critical exponents Monte Carlo

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@article{arxiv.cond-mat/9710152,
  title  = {Expansion Around the Mean-Field Solution of the Bak-Sneppen Model},
  author = {Matteo Marsili and Paolo De Los Rios and Sergei Maslov},
  journal= {arXiv preprint arXiv:cond-mat/9710152},
  year   = {2009}
}

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5 pages, 2 ps-figures icluded

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

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