Critical dynamics of the body-centered-cubic classical Heisenberg antiferromagnet.

Abstract

We have used spin dynamics techniques to perform large-scale simulations of the dynamic behavior of the L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}L body-centered-cubic classical Heisenberg antiferromagnet with L\ensuremath{\le}48 at a range of temperatures above and below as well as at the critical point ${\mathit{T}}_{\mathit{c}}$. The temporal evolutions of the spin configurations were determined numerically from coupled equations of motion for individual spins by a fourth-order predictor-corrector method, with initial spin configurations generated by Monte Carlo simulations. The neutron scattering function S(q,\ensuremath{\omega}) was calculated from the space- and time-displaced spin-spin correlation function. We used a previously developed dynamic finite-size scaling theory to extract the dynamic critical exponent z from S(q,\ensuremath{\omega}) at ${\mathit{T}}_{\mathit{c}}$. Our results are in agreement with the theoretical prediction of z=1.5 and with experimental results; however, we find that the asymptotic regime was only entered at L\ensuremath{\approxeq}30. In the analysis of the form of the transverse and longitudinal components of S(q,\ensuremath{\omega}) we found that a central diffusion peak appears below ${\mathit{T}}_{\mathit{c}}$ predominantly in the longitudinal component and remains present through and above ${\mathit{T}}_{\mathit{c}}$. The transverse component of the spin-wave peak is Lorentzian below ${\mathit{T}}_{\mathit{c}}$ but for T\ensuremath{\geqslant}${\mathit{T}}_{\mathit{c}}$ is described best by a more complex functional form. Below ${\mathit{T}}_{\mathit{c}}$ we see evidence of multiple spin-wave peaks in the longitudinal component. \textcopyright{} 1996 The American Physical Society.