  A scalar theory can have many Gaussian (free) fixed points, corresponding to
Lagrangians of the form $\phi\,\Box^k\phi$. We use the non-perturbative RG to
study examples of flows between such fixed points. We show that the anomalous
dimension changes continuously in such a way that at the endpoints the fields
have the correct dimensions of the respective free theories. These models
exhibit various pathologies, but are nonetheless interesting as examples of
theories that are asymptotically free both in the infrared and in the
ultraviolet. Furthermore, they illustrate the fact that a diverging coupling
can actually correspond to a free theory.
