Critical dynamics of isotropic antiferromagnets using renormalization-group methods:T≥TN

We study a model equation of motion describing the dynamics of isotropic antiferromagnets near the critical point. We perform a renormalization-group analysis of this equation of motion correct to $O\left(\epsilon \right)$, where $\epsilon =4-d$, finding recursion relations and analyzing their fixed points and their stability. For the one stable fixed point we obtain the dynamical index $z=\frac{d}{2}=2-\frac{\epsilon }{2}$. We also calculate the response and correlation functions in the scaling region using perturbation theory correct to $O\left(\epsilon \right)$. Our calculation gives analytical forms for the correlation functions for the staggered magnetization and the magnetization. These correlation functions can be written in the dynamical scaling form. The shape function that characterizes the frequency spectrum for the staggered magnetization is Lorentzian in the hydrodynamical regime, but shows fluctuation induced peaks at and near the N†eel temperature. The shape function for the magnetization is essentially Lorentzian for all $x=q\xi$ (where $q$ is the wave number and $\xi$ is the correlation length) and shows a narrow lydrodynamical width as $x\to 0$.