Critical exponents of the anisotropic Bak-Sneppen model

Details Critical exponents of the anisotropic Bak-Sneppen model Critical exponents of the anisotropic Bak-Sneppen model

1998-03-05

arxiv.org/abs/cond-mat/9803068v2

Phys. Rev. E 58, 7141-7145 (1998).

Physics

Condensed Matter

Statistical Mechanics

8 pages, three figures included with psfig, some rewriting, + extra figure and table of exponents

Scientific paper

10.1103/PhysRevE.58.7141

We analyze the behavior of spatially anisotropic Bak-Sneppen model. We demonstrate that a nontrivial relation between critical exponents tau and mu=d/D, recently derived for the isotropic Bak-Sneppen model, holds for its anisotropic version as well. For one-dimensional anisotropic Bak-Sneppen model we derive a novel exact equation for the distribution of avalanche spatial sizes, and extract the value gamma=2 for one of the critical exponents of the model. Other critical exponents are then determined from previously known exponent relations. Our results are in excellent agreement with Monte Carlo simulations of the model as well as with direct numerical integration of the new equation.

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