Renormalized $g-log (g)$ double expansion for the invariant $\phi^4$-trajectory in three dimensions

Abstract

We study the invariant unstable manifold of the trivial renormalization group fixed point tangent to the $\phi^{4}$-vertex in three dimensions. We parametrize it by a running $\phi^{4}$-coupling with linear step $\beta$-function. It is shown to have a renormalized double expansion in the running coupling and its logarithm.