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

Abstract

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')^ϕwell inside the scaling regime, the spin autocorrelation function behaves like <s(t)s(t')> = L(t')^{-(d-2+η)} [L(t')/L(t)]^{λ_c}. For the O(n) model in the n -> \infty limit, we show that λ_c=d+2 and ϕ=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.

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