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Authors
Marco Zannetti
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The Chapter is devoted to reviewing the main features of aging in non disordered systems relaxing via domain growth, after an istantaneous temperature quench. Using the autocorrelation and autoresponse functions to gauge the deviation from equilibrium, an hierarchy of processes is obtained by changing the temperature of the quench and the space dimensionality. The special role of the lower critical dimensionality is highlighted. Basic properties like the separation of the time scales and the splitting of degrees of freedom into fast and slow variables are treated in detail, both in general terms and through analytical calculations in solvable models. Though domain growth is believed to be a well understood paradigma of slow relaxation, emphasis of this review is on the non trivial aspects, not yet fully clarified, like the response function scaling behavior.
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We have used molecular dynamics simulations for a comprehensive study of phase separation in a two-dimensional single component off-lattice model where particles interact through the Lennard-Jones potential. Via state-of-the-art methods we have analyzed simulation data on structure, growth and aging for nonequilibrium evolutions in the model. These data were obtained following quenches of well-equilibrated homogeneous configurations, with density close to the critical value, to various temperatures inside the miscibility gap, having vapor-liquid as well as vapor-solid coexistence. For the vapor-liquid phase separation we observe that $ell$, the average domain length, grows with time ($t$) as $t^{1/2}$, a behavior that has connection with hydrodynamics. At low enough temperature, a sharp crossover of this time dependence to a much slower, temperature dependent, growth is identified within the time scale of our simulations, implying solid-like final state of the high density phase. This crossover is, interestingly, accompanied by strong differences in domain morphology and other structural aspects between the two situations. For aging, we have presented results for the order-parameter autocorrelation function. This quantity exhibits data-collapse with respect to $ell/ell_w$, $ell$ and $ell_w$ being the average domain lengths at times $t$ and $t_w$ ($leq t$), respectively, the latter being the age of a system. Corresponding scaling function follows a power-law decay: $~sim (ell/ell_w)^{-lambda}$, for $tgg t_w$. The decay exponent $lambda$, for the vapor-liquid case, is accurately estimated via the application of an advanced finite-size scaling method. The obtained value is observed to satisfy a bound.
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A stochastic genetic model for biological aging is introduced bridging the gap between the bit-string Penna model and the Pletcher-Neuhauser approach. The phenomenon of exponentially increasing mortality function at intermediate ages and its deceleration at advanced ages is reproduced for both the evolutionary steady-state population and the genetically homogeneous individuals.
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The goal of this work is to show that a ferromagnetic-like domain growth process takes place within the backbone of the three-dimensional $pm J$ Edwards-Anderson (EA) spin glass model. To sustain this affirmation we study the heterogeneities displayed in the out-of-equilibrium dynamics of the model. We show that both correlation function and mean flipping time distribution present features that have a direct relation with spatial heterogeneities, and that they can be characterized by the backbone structure. In order to gain intuition we analyze the pure ferromagnetic Ising model, where we show the presence of dynamical heterogeneities in the mean flipping time distribution that are directly associated to ferromagnetic growing domains. We extend a method devised to detect domain walls in the Ising model to carry out a similar analysis in the three-dimensional EA spin glass model. This allows us to show that there exists a domain growth process within the backbone of this model.
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