  We study an active random walker model in which a particle's motion is
determined by a self-generated field. The field encodes information about the
particle's path history. This leads to either self-attractive or self-repelling
behavior. For self-repelling behavior, we find a phase transition in the
dynamics: when the coupling between the field and the walker exceeds a critical
value, the particle's behavior changes from renormalized diffusion to one
characterized by a diverging diffusion coefficient. The dynamical behavior for
all cases is surprisingly independent of dimension and of the noise amplitude.
