d_c=4 is the upper critical dimension for the Bak-Sneppen model

Details d_c=4 is the upper critical dimension for the Bak-Sneppen model d_c=4 is the upper critical dimension for the Bak-Sneppen model

1999-11-18

arxiv.org/abs/cond-mat/9911273v2

Phys. Rev. Lett, 84 (2000) 2267

Physics

Condensed Matter

Statistical Mechanics

4 pages, RevTex4, as to appear in Phys. Rev. Lett., related papers available at http://userwww.service.emory.edu/~sboettc/

Scientific paper

10.1103/PhysRevLett.84.2267

Numerical results are presented indicating d_c=4 as the upper critical dimension for the Bak-Sneppen evolution model. This finding agrees with previous theoretical arguments, but contradicts a recent Letter [Phys. Rev. Lett. 80, 5746-5749 (1998)] that placed d_c as high as d=8. In particular, we find that avalanches are compact for all dimensions d<=4, and are fractal for d>4. Under those conditions, scaling arguments predict a d_c=4, where hyperscaling relations hold for d<=4. Other properties of avalanches, studied for 1<=d<=6, corroborate this result. To this end, an improved numerical algorithm is presented that is based on the equivalent branching process.

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