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

Non-equilibrium quasi-long-range order of driven random field O(N) model