sAvalanche distribution in the Feder and Feder model: Effects of quenched disorder

The Feder and Feder earthquake model shows an integrated size distribution of events that decays as a power law when averaged over realizations with different initial conditions. The question remains as to what is the distribution for a single realization. Small amounts of quenched disorder can break the symmetries of the Feder and Feder model, introduce stochasticity in the dynamics, and allow for self-averaging. The introduction of weak frozen spatial disorder reveals a dynamical behavior very different from what is seen by ensemble averaging. The resulting integrated size distribution seems to be a function of the logarithm of the size, P(n)∼(log ${}_{10}{}^{}{}_{}{}^{}\mathrm{n}$${)}^{\mathrm{-}\nu }$.