Theory of Self-organized Criticality for Problems with Extremal Dynamics
arXiv:cond-mat/9702176 · doi:10.1209/epl/i1997-00273-1
Abstract
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.
11 pages Latex (revtex), 3 postscript figures included. Submitted to Europhys. Lett