d_c=4 is the upper critical dimension for the Bak-Sneppen model
Abstract
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.
Cite
@article{arxiv.cond-mat/9911273,
title = {d_c=4 is the upper critical dimension for the Bak-Sneppen model},
author = {S. Boettcher and M. Paczuski},
journal= {arXiv preprint arXiv:cond-mat/9911273},
year = {2009}
}
Comments
4 pages, RevTex4, as to appear in Phys. Rev. Lett., related papers available at http://userwww.service.emory.edu/~sboettc/