Autocorrelation exponent of conserved spin systems in the scaling regime following a critical quench
Résumé
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 $\\sim L(t\')^{-(d-2+\\eta)}[{L(t\')}/{L(t)}]^{\\lambda^\\prime_c}$. For the O(n) model in the $n\\to\\infty$ limit, we show that $\\lambda^\\prime_c=d+2$ 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.