Spin-dynamics study of the dynamic critical behavior of the three-dimensional classical Heisenberg ferromagnet

Abstract

Using spin-dynamics techniques we have performed large-scale computer 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 ferromagnet with L\ensuremath{\le}40 in the vicinity of the critical point ${\mathit{T}}_{\mathit{c}}$. The temporal evolutions of 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 methods. The space- and time-displaced spin-spin correlation functions and their space-time Fourier transforms were calculated to determine the neutron-scattering functions. We developed a dynamic finite-size scaling theory for the neutron-scattering function at ${\mathit{T}}_{\mathit{c}}$ and used it to extract the dynamic critical exponent z. Within our resolution limit, the value of z was estimated to be 2.478(28), in excellent agreement with the dynamic scaling prediction, and dynamic scaling was found to be valid for momentum transfer q up to 0.4\ensuremath{\pi} in the (1,0,0) direction.