Fixed points of the dissipative Hofstadter model.

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 binding 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 nontrivial 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.