  We compute the dynamic structure factor for the Ising model with a purely
relaxational dynamics (model A). We perform a perturbative calculation in the
$\epsilon$ expansion, at two loops in the high-temperature phase and at one
loop in the temperature magnetic-field plane, and a Monte Carlo simulation in
the high-temperature phase. We find that the dynamic structure factor is very
well approximated by its mean-field Gaussian form up to moderately large values
of the frequency $\omega$ and momentum $k$. In the region we can investigate,
$k\xi \lesssim 5$, $\omega \tau \lesssim 10$, where $\xi$ is the correlation
length and $\tau$ the zero-momentum autocorrelation time, deviations are at
most of a few percent.
