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We study the autocorrelation function of a conserved spin system following aquench at the critical temperature. Defining the correlation length L(t)\simt^{1/z}, we find that for times t' and t satisfying L(t') << L(t) << L(t')^\phiwell inside the scaling regime, the spin autocorrelation function behaves like<s(t)s(t')> = L(t')^{-(d-2+\eta)} [L(t')/L(t)]^{\lambda_c}. For the O(n) modelin the n -> \infty limit, we show that \lambda_c=d+2 and \phi=z/2. We give aheuristic argument suggesting that this result is in fact valid for anydimension d and spin vector dimension n. We present numerical simulations forthe conserved Ising model in d=1 and d=2, which are fully consistent with thepresent theory.Comment: Published version; Two typos corrected in Eq. (7) and and Eq. (11

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