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Mean field theory of self-organized critical phenomena. (English) Zbl 1086.82530

Summary: A mean field theory is presented for the recently discovered self-organized critical phenomena. The critical exponents are calculated and found to be the same as the mean field values for percolation. The power spectrum has “\(1/f\)” behavior with exponent \(\varphi=1\).

MSC:

82B27 Critical phenomena in equilibrium statistical mechanics
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References:

[1] P. Bak, C. Tang, and K. Wiesenfeld,Phys. Rev. Lett. 59:381 (1987);Phys. Rev. A (1988).
[2] C. Tang and P. Bak,Phys. Rev. Lett., submitted.
[3] L. Wu, S. Zhou, C. Liu, L. Kadanoff, and S. Nagel,Bull. Amer. Phys. Soc. 33:534 (1988).
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