Coarsening dynamics of an isotropic ferromagnetic superfluid

In zero magnetic field the ground state manifold of a ferromagnetic spin-1 condensate is SO(3) and exhibits $\mathbb{Z}_2$ vortices as topological defects. We investigate the phase ordering dynamics of this system after being quenched into this ferromagnetic phase from a zero temperature unmagnetized phase. Following the quench, we observe the ordering of both magnetic and gauge domains. We find that these domains grow diffusively, i.e. with domain size $L(t)\sim t^{1/2}$, and exhibit dynamic scale invariance. The coarsening dynamics progresses as $\mathbb{Z}_2$ vortices annihilate, however we find that at finite energy a number of these vortices persist in small clumps without influencing magnetic or gauge order. We consider the influence of a small non-zero magnetic field, which reduces the ground state symmetry, and show that this sets a critical length scale such that when the domains reach this size the system dynamically transitions in order parameter and scaling behaviour from an isotropic to an anisotropic ferromagnetic superfluid.