Renormalization Group Functions of \phi^4 Theory from High-Temperature Expansions

TL;DR

This paper calculates the renormalization group functions of four-dimensional ^4 theory using high-temperature expansions of the Ising model, achieving high accuracy across a range of coupling constants.

Contribution

It introduces a method to derive RG functions from high-temperature expansions, extending calculations up to the 13th order in inverse square root of the coupling.

Findings

RG functions computed with 10^{-4} accuracy for (g)

Anomalous dimensions with 10^{-3} to 10^{-2} accuracy

Expansions extended to 13th order in g^{-1/2}

Abstract

It has been previously shown that calculation of renormalization group (RG) functions of the scalar \phi^4 theory reduces to the analysis of thermodynamic properties of the Ising model. Using high-temperature expansions for the latter, RG functions of four-dimensional theory can be calculated for arbitrary coupling constant g with an accuracy 10^{-4} for the Gell-Mann - Low function \beta(g) and an accuracy 10^{-3} - 10^{-2} for anomalous dimensions. Expansions of RG functions up to the 13th order in g^{-1/2} are obtained.