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

Details 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 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

1998-09-09

arxiv.org/abs/hep-lat/9809050v1

Helv.Phys.Acta 72 (1999) 445-483

Physics

High Energy Physics

High Energy Physics - Lattice

42 pages LaTeX2e

Scientific paper

We study the renormalization invariant trajectory of the $\phi^4$-perturbation of the free field fixed point in the hierarchical approximation. We parametrize it by a running $\phi^4$-coupling $g$ with linear step $\beta$-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 $g$.

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