Scale-free distributions in nature: an overview of self-organized criticality

Ronald Dickman
Federal University of Minas Gerais

Following a brief review of power-law distributions in nature, I shall explain why such observations pose a challenge for statistical physics, and the paradigm of self-organized criticality (SOC), introduced by Per Bak and coworkers [1]. SOC shows how scale-free event distributions can arise in the apparent absence of tuning parameters, in a system of many interacting entities, each having a threshold for relaxation, under a slow external drive. A similar mechanism has been suggested to underly power-law distributions of rain and drought [2]. SOC in its most familiar context, the "sandpile" models, is connected with a phase transition to an absorbing state [3]. I shall also discuss the generation of apparent power-law distributions via chaotic advection [4].

1. P. Bak, C. Tang, and K. Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987).

2. O. Peters, C. Hertlein, and K. Christensen, Phys. Rev. Lett. 88,
018701 (2002); O. Peters and K. Christensen, Phys. Rev. E 66, 036120

3. R. Dickman, M. A. Muñoz, A. Vespignani, and S. Zapperi, Braz. J. Phys.
30, (2000) 27.

4. R. Dickman, Phys. Rev. Lett. 90, 108701 (2003).

Presentation (PDF File)

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