Dynamic structure factor of the Ising model with purely relaxational dynamics

Abstract

We compute the dynamic structure factor for the Ising model with a purely relaxational dynamics (model A). We perform a perturbative calculation in the $ε$ 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 $ω$ and momentum $k$. In the region we can investigate, $kξ\lesssim 5$, $ωτ\lesssim 10$, where $ξ$ is the correlation length and $τ$ the zero-momentum autocorrelation time, deviations are at most of a few percent.