  We discuss the O(2N) vector model in three dimensions. While this model flows
to the Wilson-Fisher fixed point when fine tuned, working in a double-scaling
limit of large N and large charge allows us to study the model away from the
critical point and even to follow the RG flow from the UV to the IR. The
crucial observation is that the effective potential -- at leading order in N
but exact to all orders in perturbation theory -- is the Legendre transform of
the grand potential at fixed charge. This allows us to write an effective
action and the free energy for generic values of the coupling in a very simple
fashion and without evaluating any Feynman diagrams.
