arXiv:cond-mat/0404203 · Physical Review B

Aging phenomena in critical semi-infinite systems

Michel Pleimling

Published Sep 3, 2004• 34 citations

Abstract

Nonequilibrium surface autocorrelation and autoresponse functions are studied numerically in semi-infinite critical systems in the dynamical scaling regime. Dynamical critical behavior is examined for a nonconserved order parameter in semi-infinite two- and three-dimensional Ising models as well as in the Hilhorst--van Leeuwen model. The latter model permits a systematic study of surface aging phenomena, as the surface critical exponents change continuously as function of a model parameter. The scaling behavior of surface two-time quantities is investigated and scaling functions are confronted with predictions coming from the theory of local scale invariance. Furthermore, surface fluctuation-dissipation ratios are computed and their asymptotic values are shown to depend on the values of surface critical exponents.

DOI: 10.1103/physrevb.70.104401

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arXiv:cond-mat/0404203 · Physical Review B

Aging phenomena in critical semi-infinite systems

Michel Pleimling

Published Sep 3, 2004• 34 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevb.70.104401

Related papers

Spin Systems far from Equilibrium: Aging and Dynamic Phase Transition

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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 }

|⁠.

In situations such as phase ordering or non-equilibrium critical dynamics, the two-time autoresponse function scales as

R(t,s)\\approx s^{-1-a} F_2(t/s)

, where

a

is a known exponent. For any value of the dynamical exponent

z

, we argue that this dynamical scaling can be extended towards conformal invariance. Thus the scaling function

F_2

is determined. This prediction is confirmed by several examples, both for

T<T_c

and at

T=T_c

: the two- and three-dimensional kinetic Ising model with Glauber dynamics is studied numerically, while exact results are available for the kinetic spherical model with a non-conserved order parameter, both for short-ranged and long-ranged interactions, as well as for the mean-field spherical spin glass.

b

and the nonequilibrium autocorrelation decay exponent ${\ensuremath{\lambda}}_{c}/{z}_{c}$. We also analyze the fluctuation-dissipation relationship at the critical temperature, obtaining the critical fluctuation-dissipation ratio ${X}_{\ensuremath{\infty}}$. By comparing our results with the aging scaling reported previously for a model of interacting flux lines in the vortex-glass regime, we found that the exponents for both models are very different.