  The phase diagram of a dissipative particle in a periodic potential and a
magnetic field is studied in the weak barrier limit and in the tight-biding
regime. For the case of half flux per plaquette, and for a wide range of values
of the dissipation, the physics of the model is determined by a non trivial
fixed point. A combination of exact and variational results is used to
characterize this fixed point. Finally, it is also argued that there is an
intermediate energy scale that separates the weak coupling physics from the
tight-binding solution.
