Renormalization group functions of the φ4 theory from high-temperature expansions

It has been previously shown that calculation of the renormalization group (RG) functions of scalar φ4 theory reduces to analysis of thermodynamic properties of the Ising model. Using high-temperature expansions for the latter, RG functions of the four-dimensional theory can be calculated for arbitrary coupling constant g with an accuracy of 10−4 for the Gell-Mann-Low function β(g) and with an accuracy of 10−3–10−2 for anomalous dimensions. The expansions of the renormalization group functions up to the 13th order in g−1/2 have been obtained.