FACULTY AND RESEARCH

A new model of self-organized criticality (SOC) is described which differs from ordinary sand-pile SOC models in that it uses electrically charged particles of different kinds to propagate activities and to generate the critical state. The model, arguably called the e-pile model (as an alternative to sand-pile, with “e-” standing for “electric charge”), is motivated by the problem of dielectric relaxation in self-asembling random lattices with disorder under the action of electrostatic forces, but in principle it may be applied to different SOC processes with the random injection scheme and charitable lattice-redistribution rule. We show that the critical state is that of self-evolving random percolation clusters at the edge of percolation and is also different from known “self-organized” versions of the percolation problem based on the directed percolation. A set of critical exponents is obtained based on the random walks, using the Kramers-Kronig relation and the formalism of frequency-dependent complex conductivity. The relaxation of a supercritical system to SOC is shown to obey the Mittag-Leffler pattern and fractional relaxation equation, with a broad distribution of durations of relaxation events.