Dynamic structure factor of the Ising model with purely relaxational dynamics

TL;DR

This paper calculates the dynamic structure factor of the Ising model with relaxational dynamics using perturbative and Monte Carlo methods, showing it closely matches mean-field predictions with minor deviations.

Contribution

It provides a detailed perturbative and simulation analysis of the dynamic structure factor for the Ising model with purely relaxational dynamics, extending understanding beyond mean-field approximations.

Findings

Dynamic structure factor closely matches Gaussian form up to moderate frequencies and momenta.

Deviations from mean-field are at most a few percent in the investigated region.

Perturbative calculations agree well with Monte Carlo simulations.

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 $\epsilon$ 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.