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.

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

References in corpus (2)

• Extremal Optimization of Graph Partitioning at the Percolation Threshold
• On the High-dimensional Bak-Sneppen model

Cited by in corpus (8)

• Bak-Sneppen model near zero dimension
• On the thresholds, probability densities, and critical exponents of Bak-Sneppen-like models
• On singular probability densities generated by extremal dynamics
• Branching Process in a Stochastic Extremal Model
• Asymmetric dynamics and critical behavior in the Bak-Sneppen model
• Absorbing-state phase transitions with extremal dynamics
• Universal persistence exponents in an extremally driven system
• Critical behavior of a stochastic anisotropic Bak-Sneppen model