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

Details 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

2004-06-15

arxiv.org/abs/cond-mat/0406333v2

Phys. Rev. Lett. 93, 130602 (2004)

Physics

Condensed Matter

Statistical Mechanics

Published version; Two typos corrected in Eq. (7) and and Eq. (11)

Scientific paper

10.1103/PhysRevLett.93.130602

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') << L(t) << L(t')^\phi well inside the scaling regime, the spin autocorrelation function behaves like = L(t')^{-(d-2+\eta)} [L(t')/L(t)]^{\lambda_c}. For the O(n) model in the n -> \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 the present theory.

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