dc = 4 is the upper critical dimension for the Bak-Sneppen model.
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 (1998)] that placed d(c) as high as d = 8. In particular, we find that avalanches are compact for all dimensions d< or =4 and are fractal for d>4. Under those conditions, scaling arguments predict a d(c) = 4, where hyperscaling relations hold for d< or =4. Other properties of avalanches, studied for 1< or =d< or =6, corroborate this result. To this end, an improved numerical algorithm is presented that is based on the equivalent branching process.
Boettcher
S
S
Physics Department, Emory University, Atlanta, Georgia 30322, USA.
Paczuski
M
M
D000465:Algorithms; D005075:Biological Evolution; D008962:Models, Theoretical