Electrons in an annealed environment: A special case of the interacting electron problem

The problem of noninteracting electrons in the presence of annealed magnetic disorder, in addition to nonmagnetic quenched disorder, is considered. It is shown that the proper physical interpretation of this model is one of electrons interacting via a potential that is long-ranged in time, and that its technical analysis by means of renormalization group techniques must also be done in analogy to the interacting problem. As a result, and contrary to previous claims, the model does not simply describe a metal-insulator transition in $d=2+\epsilon$ ($\epsilon\ll 1$) dimensions. Rather, it describes a transition to a ferromagnetic state that, as a function of the disorder, precedes the metal-insulator transition close to $d=2$. In $d=3$, a transition from a paramagnetic metal to a paramagnetic insulator is possible.