Dynamics of Ordering of Heisenberg Spins with Torque --- Nonconserved Case. I

Abstract

We study the dynamics of ordering of a nonconserved Heisenberg magnet. The dynamics consists of two parts --- an irreversible dissipation into a heat bath and a reversible precession induced by a torque due to the local molecular field. For quenches to zero temperature, we provide convincing arguments, both numerically (Langevin simulation) and analytically (approximate closure scheme due to Mazenko), that the torque is irrelevant at late times. We subject the Mazenko closure scheme to systematic numerical tests. Such an analysis, carried out for the first time on a vector order parameter, shows that the closure scheme performs respectably well. For quenches to $T_c$, we show, to ${\cal O}(ε^2)$, that the torque is irrelevant at the Wilson-Fisher fixed point.