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Accueil du site > Publications > Publications 2004 > Autocorrelation exponent of conserved spin systems in the scaling regime following a critical quench

Autocorrelation exponent of conserved spin systems in the scaling regime following a critical quench

Clément Sire

par Clément Sire - 11 avril 2006

We study the autocorrelation function of a conserved spin system following a quench at the critical temperature. Defining the correlation length L(t)\sim t^{1/z}, we find that for times t' and t satisfying L(t') \ll L(t) \ll L(t')^\phi well inside the scaling regime, the autocorrelation function behaves like <s(t)s(t')> \sim L(t')^{-(d-2+\eta)} [{L(t')}/{L(t)}]^{\lambda'_c}. For the O(n) model in the n\to\infty limit, we show that \lambda'_c=d+2 and \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 this result.

Preprint : http://arxiv.org/abs/cond-mat/0406333