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We discuss the interplay between the degree of dynamical stochasticity,memory persistence and violation of the self-averaging property in the agingkinetics of quenched ferromagnets. We show that, in general, the longestpossible memory effects, which correspond to the slowest possible temporaldecay of the correlation function, are accompanied by the largest possibleviolation of self-averaging and a quasi-deterministic descent into the ergodiccomponents. This phenomenon is observed in different systems, such as the Isingmodel with long-range interactions, including mean-field, and the short-rangerandom field Ising model.

Quasi-deterministic dynamics, memory effects, and lack of self-averaging in the relaxation of quenched ferromagnets