Renormalization Group flows between Gaussian Fixed Points

A scalar theory can have many Gaussian (free) fixed points, corresponding to Lagrangians of the form $\phi {\mathrm{\square }}^k\phi$. 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.