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

C. Sire

Published 2004 in Physical Review Letters

ABSTRACT

We study the autocorrelation function of a conserved spin system following a quench at the critical temperature. Defining the correlation length L(t) approximately t(1/z), we find that for times t' and t satisfying L(t')<<L(t)<<L(t')(phi) well inside the scaling regime, the spin autocorrelation function behaves like s(t)s(t') approximately L(t')(-(d-2+eta))[L(t')/L(t)](lambda(')(c)). For the O(n) model in the n-->infinity 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 the present theory.

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