Aging following a zero-temperature quench in the $d=3$ Ising model

Abstract: Aging in phase-ordering kinetics of the $d=3$ Ising model following a quench from infinite to zero temperature is studied by means of Monte Carlo simulations. In this model the two-time spin-spin autocorrelator $C_\text{ag}$ is expected to obey dynamical scaling and to follow asymptotically a power-law decay with the autocorrelation exponent $\lambda$. Previous work indicated that the lower Fisher-Huse bound of $\lambda\geq d/2 = 1.5$ is violated in this model. Using much larger systems than previously studied, the instantaneous exponent for $\lambda$ we obtain at late times does \emph{not} disagree with this bound. By conducting systematic fits to the data of $C_\text{ag}$ using different ansaetze for the leading correction term, we find $\lambda = 1.58(14)$ with most of error attributed to the systematic uncertainty regarding the ansaetze. This result is in contrast to the recent report that below the roughening transition universality might be violated.