Rigorous control of the non-perturbative corrections to the double expansion in $g$ and $g^2\ln(g)$ for the $ϕ^4_3$-trajectory in the hierarchical approximation
Abstract
Description
We study the renormalization invariant trajectory of the $ϕ^4$-perturbation of the free field fixed point in the hierarchical approximation. We parametrize it by a running $ϕ^4$-coupling $g$ with linear step $β$-function. We rigorously control the non-perturbative corrections to finite order approximants from double perturbation theory in $g$ and $g^2\ln(g)$. The construction uses a contraction mapping for the extended renormalization group composed of a hierarchical block spin transformation with a flow of $g$.
42 pages LaTeX2e
42 pages LaTeX2e