Critical dynamics of the simple-cubic Heisenberg antiferromagnet RbMnF$_3$: Extrapolation to q=0

TL;DR

This study uses Monte Carlo and spin dynamics simulations to analyze the dynamic critical behavior of the simple-cubic Heisenberg antiferromagnet RbMnF$_3$, focusing on the dynamic critical exponent and the structure factor at the critical temperature.

Contribution

It provides a more accurate estimate of the dynamic critical exponent and clarifies the origin of the central peak in the dynamic structure factor at criticality.

Findings

Estimated z=1.49±0.03, aligning with theoretical predictions.

The central peak at T_c is due to the longitudinal component.

Larger lattice sizes improve understanding of asymptotic critical behavior.

Abstract

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.