Thermal shifts and intermittent linear response of aging systems

At time $t$ after an initial quench, an aging system responds to a perturbation turned on at time $t_{\rm w} < t$ in a way mainly depending on the number of intermittent energy fluctuations, so-called quakes, which fall within the observation interval $(t_{\rm w},t]$ [Sibani et al. Phys. Rev. B, 74, 224407 and Eur. J. of Physics B, 58,483-491, 2007]. The temporal distribution of the quakes implies a functional dependence of the average response on the ratio $t/t_{\rm w}$. Further insight is obtained imposing small temperature steps, so-called $T$-shifts. The average response as a function of $t/t_{\rm w,eff}$, where $t_{\rm w,eff}$ is the effective age, is similar to the response of a system aged isothermally at the final temperature. Using an Ising model with plaquette interactions, the applicability of analytic formulae for the average isothermal magnetization is confirmed. The $T$-shifted aging behavior of the model is described using effective ages. Large positive shifts nearly reset the effective age. Negative $T$-shifts offer a more detailed probe of the dynamics. Assuming the marginal stability of the `current' attractor against thermal noise fluctuations, the scaling form $t_{\rm w,eff} = t_{\rm w}^x$, and the dependence of the exponent $x$ on the aging temperatures before and after the shift are theoretically available. The predicted form of $x$ has no adjustable parameters. Both the algebraic scaling of the effective age and the form of the exponent agree with the data. The simulations thus confirm the crucial r\^{o}le of marginal stability in glassy relaxation.