Reply to Comment on "Fluctuation-dissipation relations in the non-equilibrium critical dynamics of Ising models"

TL;DR

This paper defends previous findings that the fluctuation-dissipation ratio in non-equilibrium critical Ising models can be accurately measured using certain observables, countering critiques and emphasizing the advantages of coherent observables.

Contribution

The authors demonstrate that their method for measuring the fluctuation-dissipation ratio remains valid and effective, even when challenged by alternative interpretations, and compare results with renormalization-group predictions.

Findings

Data show genuine two-time dependence of X(t,tw).

Fluctuation-dissipation plots are close to a straight line.

Coherent observables facilitate easier measurement of $ ext{X}_ ext{in}$.

Abstract

We have recently shown that in non-equilibrium spin systems at criticality the limit $\Xin$ of the fluctuation-dissipation ratio X(t,tw) for t >> tw >> 1 can be measured using observables such as magnetization or energy [Phys. Rev.\ E {\bf 68}, 016116 (2003)]. Pleimling argues in a Comment [cond-mat/0309652] on our paper that for such observables correlation and response functions are dominated by one-time quantities dependent only on t, and are therefore not suitable for a determination of $\Xin$. Using standard scaling forms of correlation and response functions, as used by Pleimling, we show that our data do have a genuine two-time dependence and allow X(t,tw) and $\Xin$ to be measured, so that Pleimling's criticisms are easily refuted. We also compare with predictions from renormalization-group calculations, which are consistent with our numerical observation of a fluctuation-dissipation plot for the magnetization that is very close to a straight line. A key point remains that coherent observables make measurements of $\Xin$ easier than the traditionally used incoherent ones, producing fluctuation-dissipation plots whose slope is close to $\Xin$ over a much larger range.