  We investigate three-dimensional O(N) spin models driven with a uniform
velocity over a random field. Within a spin-wave approximation, it is shown
that in the strong driving regime the model with N=2 exhibits a
quasi-long-range order in which the spatial correlation function decays in a
power-law form. Furthermore, for the cases that N=2 and 3, we numerically
demonstrate a non-equilibrium phase transition between the quasi-long-range
order phase and the disordered phase, which turns out to resemble the
Kosterlitz-Thouless transition in the two-dimensional pure XY model in
equilibrium.
