  We consider magnetic friction between two systems of $q$-state Potts spins
which are moving along their boundaries with a relative constant velocity $v$.
Due to the interaction between the surface spins there is a permanent energy
flow and the system is in a steady state which is far from equilibrium. The
problem is treated analytically in the limit $v=\infty$ (in one dimension, as
well as in two dimensions for large-$q$ values) and for $v$ and $q$ finite by
Monte Carlo simulations in two dimensions. Exotic nonequilibrium phase
transitions take place, the properties of which depend on the type of phase
transition in equilibrium. When this latter transition is of first order, a
sequence of second- and first-order nonequilibrium transitions can be observed
when the interaction is varied.
