Critical dynamics of the simple-cubic Heisenberg antiferromagnet RbMnF₃: Extrapolation to q=0

Monte Carlo and spin dynamics simulations have been used to study the dynamic critical behavior of RbMnF$_3$, treated as a classical Heisenberg antiferromagnet on a simple cubic lattice. In an attempt to understand the difference in the value of the dynamic critical exponent $z$ between experiment and theory, we have used larger lattice sizes than in our previous simulations to better probe the asymptotic critical region in momentum. We estimate $z=1.49\pm 0.03$, in good agreement with the renormalization-group theory and dynamic scaling predictions. In addition, the central peak in the dynamic structure factor at $T_c$, seen in experiments and previous simulations, but absent in the renomalization-group and mode-coupling theories, is shown to be solely in the longitudinal component.