1999/11/30 by Stefan Boettcher, S. Boettcher, Maya Paczuski +1 · 1 citation
Materials Science · Mathematics · Physics and Astronomy · #Material Dynamics and Properties #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevlett.84.2267
published as Phys. Rev. Lett, 84 (2000) 2267 · 4 pages, RevTex4, as to appear in Phys. Rev. Lett., related papers available at http://userwww.service.emory.edu/~sboettc/
arxiv created 2000/01/15 · openalex publication_date 2000/03/06 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Numerical results are presented indicating dc\phantom\rule0ex0ex=\phantom\rule0ex0ex4 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 dc as high as d\phantom\rule0ex0ex=\phantom\rule0ex0ex8. In particular, we find that avalanches are compact for all dimensions d\ensuremath≤4 and are fractal for d>4. Under those conditions, scaling arguments predict a dc\phantom\rule0ex0ex=\phantom\rule0ex0ex4, where hyperscaling relations hold for d\ensuremath≤4. Other properties of avalanches, studied for 1\ensuremath≤d\ensuremath≤6, corroborate this result. To this end, an improved numerical algorithm is presented that is based on the equivalent branching process.