Theory of Self-organized Criticality for Problems with Extremal Dynamics

Details Theory of Self-organized Criticality for Problems with Extremal Dynamics Theory of Self-organized Criticality for Problems with Extremal Dynamics

1997-02-19

arxiv.org/abs/cond-mat/9702176v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

11 pages Latex (revtex), 3 postscript figures included. Submitted to Europhys. Lett

Scientific paper

10.1209/epl/i1997-00273-1

We introduce a general theoretical scheme for a class of phenomena characterized by an extremal dynamics and quenched disorder. The approach is based on a transformation of the quenched dynamics into a stochastic one with cognitive memory and on other concepts which permit a mathematical characterization of the self-organized nature of the avalanche type dynamics. In addition it is possible to compute the relevant critical exponents directly from the microscopic model. A specific application to Invasion Percolation is presented but the approach can be easily extended to various other problems.

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