Conserved Ordering Dynamics of Heisenberg Spins with Torque

TL;DR

This paper investigates how torque influences the zero-temperature ordering dynamics of conserved Heisenberg spins, revealing a new fixed point with distinct critical exponents and highlighting the limitations of Gaussian closure theories.

Contribution

It demonstrates that torque induces a new fixed point in the dynamics of conserved Heisenberg spins and shows the inadequacy of Gaussian closure approximations.

Findings

Torque drives a new fixed point with z=2 and λ≈5.15 at zero temperature.

Gaussian closure theories are inconsistent even without torque.

Torque remains relevant at critical temperature quenches, affecting critical exponents.

Abstract

We show that a torque induced by the local molecular field drives the zero-temperature ordering dynamics of a conserved Heisenberg magnet to a new fixed point, characterised by exponents z=2 and $\lambda \approx 5.15$. Numerical solutions of the Langevin equation indicate that theories using a Gaussian closure are inconsistent even when the torque is absent. The torque is relevant even for quenches to T_c, with exponents $z=4-\epsilon/2$ and $\lambda = d$ (where $\epsilon = 6-d$). Indeed $\lambda$ is always equal to d for quenches to T_c whenever the order parameter is conserved.