Universal effective action for O(n)-symmetric \lambda \phi^4 model from renormalization group

TL;DR

This paper calculates higher-order coupling constants for the 3D n-vector model using renormalization group expansions, providing precise estimates for g_6 and discussing the challenges in estimating g_8.

Contribution

It presents 4-loop and 3-loop RG calculations for g_6 and g_8, with improved estimates for g_6^*(n) using resummation techniques, advancing understanding of universal critical behavior.

Findings

g_6^*(n) estimates deviate less than 0.3% from exact values

RG series for g_8 are too divergent for reliable estimates

Resummation improves accuracy of g_6^* predictions

Abstract

The RG expansions for renormalized coupling constants g_6 and g_8 of the 3D n-vector model are calculated in the 4-loop and 3-loop approximations respectively. Resummation of the RG series for g_6 by the Pade-Borel-Leroy technique results in the estimates for its universal critical values g_6^*(n) which are argued to deviate from the exact numbers by less than 0.3%. The RG expansion for g_8 demonstrates stronger divergence being much less suitable for getting reliable numerical estimates.