  The non-equilibrium phase transition in driven two-dimensional Ising models
with two different geometries is investigated using Monte Carlo methods as well
as analytical calculations. The models show dissipation through fluctuation
induced friction near the critical point. We first consider high driving
velocities and demonstrate that both systems are in the same universality class
and undergo a strongly anisotropic non-equilibrium phase transition, with
anisotropy exponent \theta=3. Within a field theoretical ansatz the simulation
results are confirmed. The crossover from Ising to mean field behavior in
dependency of system size and driving velocity is analyzed using crossover
scaling. It turns out that for all finite velocities the phase transition
becomes strongly anisotropic in the thermodynamic limit.
