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

TL;DR

This paper investigates the late-time dynamics of nonconserved Heisenberg spins with torque, demonstrating through simulations and analytical methods that torque effects become negligible at zero and critical temperatures, and validating the Mazenko closure scheme for vector order parameters.

Contribution

It provides the first systematic analysis of torque effects in vector order parameter dynamics and validates the Mazenko closure scheme in this context.

Findings

Torque is irrelevant at late times for quenches to zero temperature.

Torque is irrelevant at the Wilson-Fisher fixed point for quenches to critical temperature.

The Mazenko closure scheme performs well for vector order parameters.

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 ${\cal O}(\epsilon^2)$, that the torque is irrelevant at the Wilson-Fisher fixed point.