The role of initial state and final quench temperature on the aging properties in phase-ordering kinetics

We study numerically the two-dimensional Ising model with non-conserved dynamics quenched from an initial equilibrium state at the temperature $T_i\ge T_c$ to a final temperature $T_f$ below the critical one. By considering processes initiating both from a disordered state at infinite temperature $T_i=\infty$ and from the critical configurations at $T_i=T_c$ and spanning the range of final temperatures $T_f\in [0,T_c[$ we elucidate the role played by $T_i$ and $T_f$ on the aging properties and, in particular, on the behavior of the autocorrelation $C$ and of the integrated response function $\chi$. Our results show that for any choice of $T_f$, while the autocorrelation function exponent $\lambda _C$ takes a markedly different value for $T_i=\infty$ [$\lambda _C(T_i=\infty)\simeq 5/4$] or $T_i=T_c$ [$\lambda _C(T_i=T_c)\simeq 1/8$] the response function exponents are unchanged. Supported by the outcome of the analytical solution of the solvable spherical model we interpret this fact as due to the different contributions provided to autocorrelation and response by the large-scale properties of the system. As changing $T_f$ is considered, although this is expected to play no role in the large-scale/long-time properties of the system, we show important effects on the quantitative behavior of $\chi$. In particular, data for quenches to $T_f=0$ are consistent with a value of the response function exponent $\lambda _\chi=\frac{1}{2}\lambda _C(T_i=\infty)=5/8$ different from the one [$\lambda _\chi \in (0.5-0.56)$] found in a wealth of previous numerical determinations in quenches to finite final temperatures. This is interpreted as due to important pre-asymptotic corrections associated to $T_f>0$.