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arXiv:cond-mat/0406333 · Physical Review Letters

Autocorrelation Exponent of Conserved Spin Systems in the Scaling Regime Following a Critical Quench

Clément Sire

Published Sep 20, 2004• 16 citations
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Abstract

We study the autocorrelation function of a conserved spin system following a quench at the critical temperature. Defining the correlation length $L(t)\ensuremath{\sim}{t}^{1/z}$, we find that for times ${t}^{\ensuremath{'}}$ and $t$ satisfying $L({t}^{\ensuremath{'}})\ensuremath{\ll}L(t)\ensuremath{\ll}L({t}^{\ensuremath{'}}{)}^{\ensuremath{\phi}}$ well inside the scaling regime, the spin autocorrelation function behaves like $\ensuremath{\langle}s(t)s({t}^{\ensuremath{'}})\ensuremath{\rangle}\ensuremath{\sim}L({t}^{\ensuremath{'}}{)}^{\ensuremath{-}(d\ensuremath{-}2+\ensuremath{\eta})}[L({t}^{\ensuremath{'}})/L(t){]}^{{\ensuremath{\lambda}}_{c}^{\ensuremath{'}}}$. For the $O(n)$ model in the $n\ensuremath{\rightarrow}\ensuremath{\infty}$ limit, we show that ${\ensuremath{\lambda}}_{c}^{\ensuremath{'}}=d+2$ and $\ensuremath{\phi}=z/2$. We give a heuristic argument suggesting that this result is, in fact, valid for any dimension $d$ and spin vector dimension $n$. We present numerical simulations for the conserved Ising model in $d=1$ and $d=2$, which are fully consistent with the present theory.

DOI
10.1103/physrevlett.93.130602

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