arXiv:cond-mat/0309652 · Physical Review E

Comment on “Fluctuation-dissipation relations in the nonequilibrium critical dynamics of Ising models”

Michel Pleimling

Published Jul 2, 2004• 12 citations

Abstract

Recently Phys. Rev. E 68, 016116 (2003)]] proposed an alternative way to compute numerically the fluctuation-dissipation ratios in nonequilibrium critical systems. Using well-known facts of nonequilibrium critical dynamics I show that the leading contributions of the quantities they consider are in fact one-time quantities which are independent of the waiting time. The ratio of these one-time quantities determines the slope of the straight lines observed in the fluctuation-dissipation plots of Mayer et al.

DOI: 10.1103/physreve.70.018101

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arXiv:cond-mat/0309652 · Physical Review E

Comment on “Fluctuation-dissipation relations in the nonequilibrium critical dynamics of Ising models”

Michel Pleimling

Published Jul 2, 2004• 12 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physreve.70.018101

Related papers

Reply to “Comment on ‘Fluctuation-dissipation relations in the nonequilibrium critical dynamics of Ising models’ ”

Peter Mayer, Ludovic Berthier, Juan P. Garrahan +1 more

We have recently shown that in nonequilibrium spin systems at criticality the limit ${X}^{\ensuremath{\infty}}$ of the fluctuation-dissipation ratio $X(t,{t}_{w})$ for $t⪢{t}_{w}⪢1$ can be measured using observables such as magnetization or energy [Phys. Rev. E 68, 016116 (2003)]. Pleimling argues in a Comment [preceding paper, Phys. Rev. 70, 018101 (2004)] 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 ${X}^{\ensuremath{\infty}}$. 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 $X(t,{t}_{w})$ and ${X}^{\ensuremath{\infty}}$ 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 ${X}^{\ensuremath{\infty}}$ easier than the traditionally used incoherent ones, producing fluctuation-dissipation plots whose slope is close to ${X}^{\ensuremath{\infty}}$ over a much larger range.We have recently shown that in nonequilibrium spin systems at criticality the limit ${X}^{\ensuremath{\infty}}$ of the fluctuation-dissipation ratio $X(t,{t}_{w})$ for $t⪢{t}_{w}⪢1$ can be measured using observables such as magnetization or energy [Phys. Rev. E 68, 016116 (2003)]. Pleimling argues in a Comment [preceding paper, Phys. Rev. 70, 018101 (2004)] 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 ${X}^{\ensuremath{\infty}}$. 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 $X(t,{t}_{w})$ and ${X}^{\ensuremath{\infty}}$ 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 ${X}^{\ensuremath{\infty}}$ easier than the traditionally used incoherent ones, producing fluctuation-dissipation plots whose slope is close to ${X}^{\ensuremath{\infty}}$ over a much larger range.

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Comment on “Critical Behavior of the Randomly Spin Diluted 2D Ising Model: A Grand Ensemble Approach”

Aernout C. D. van Enter, Christof Külske, Christian Maes

We point out that the "disorder potential" employed in the grand ensemble approach is ill-defined in considerable generality.

arXiv:cond-mat/0005176Physical Review LettersJun 26, 200016 citations

We have recently shown that in nonequilibrium spin systems at criticality the limit ${X}^{\ensuremath{\infty}}$ of the fluctuation-dissipation ratio

X(t,{t}_{w})

for

t⪢{t}_{w}⪢1

can be measured using observables such as magnetization or energy [Phys. Rev. E 68, 016116 (2003)]. Pleimling argues in a Comment [preceding paper, Phys. Rev. 70, 018101 (2004)] 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 ${X}^{\ensuremath{\infty}}$. 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,{t}_{w})

and ${X}^{\ensuremath{\infty}}$ 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 ${X}^{\ensuremath{\infty}}$ easier than the traditionally used incoherent ones, producing fluctuation-dissipation plots whose slope is close to ${X}^{\ensuremath{\infty}}$ over a much larger range.

t_{\rm w}

| and time of observation |

t - t_{\rm w}

| with |

t>t_{\rm w}

|⁠. We discuss the obtained values of the non-equilibrium exponents for the autocorrelation and response functions and values of the universal long-time limit of the fluctuation-dissipation ratio |

X^{\infty }

|⁠. Our simulation results demonstrate that the insertion of disorder leads to new values of |

X^{\infty }

| with |

X_{\rm diluted}^{\infty }>X_{\rm pure}^{\infty }

|⁠.

Available mathematical results entail the absence of a proper ordering transition taking place at finite temperature in the case

d=1,

$\ensuremath{\sigma}=1.1,$ where the authors of the article commented on find evidence of such a transition. Moreover, in contrast to the findings of the authors of the article, the case

d=2,

$\ensuremath{\sigma}=0$ entails a ground-state energy per particle diverging logarithmically with increasing sample size, hence an infinite transition temperature.