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

Abstract

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

16 pages, Latex2e

References in corpus (2)

• The renormalized ${\varphi }_4^4$-trajectory by perturbation theory in the running coupling
• The renormalized ${\varphi }_4^4$-trajectory by perturbation theory in a running coupling II: the continuous renormalization group