  A driven Ising model with friction due to magnetic correlations has recently
been proposed by Kadau et al. (Phys. Rev. Lett. 101, 137205 (2008)). The
non-equilibrium phase transition present in this system is investigated in
detail using analytical methods as well as Monte Carlo simulations. In the
limit of high driving velocities $v$ the model shows mean field behavior due to
dimensional reduction and can be solved exactly for various geometries. The
simulations are performed with three different single spin flip rates: the
common Metropolis and Glauber rates as well as a multiplicative rate. Due to
the non-equilibrium nature of the model all rates lead to different critical
temperatures at $v>0$, while the exact solution matches the multiplicative
rate. Finally, the cross-over from Ising to mean field behavior as function of
velocity and system size is analysed in one and two dimensions.
