Theory of self-organized criticality for problems with extremal dynamics
Dipartimento di Fisica, Universitá di Roma “Tor Vergata”, Via della Ricerca Scientifica 1, I-00133 Roma, Italy
2 Dipartimento di Fisica, Universitá di Roma “La Sapienza”, P.le Aldo Moro 2, I-00185 Roma, Italy; and INFM, unitá di Roma I
3 Institut de Physique Theorique Universitè de Fribourg, Pérolles CH-1700 Fribourg, Suisse
Accepted: 3 May 1997
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.
PACS: 02.50.-r – Probability theory, stochastic processes, and statistics / 05.40.+j – Fluctuation phenomena, random processes, and Brownian motion / 05.90.+m – Other topics in statistical physics and thermodynamics
© EDP Sciences, 1997