Five-Loop Renormalization Group Functions of ø4-Theory With O(N)-Symmetric and Cubic Interactions

Abstract

The renormalization group functions are calculated in D = 4 −ε dimensions for a ø⁴- theory with two coupling constants: ${g_1}{\left( {\sum\nolimits_\alpha ^N {\varphi _\alpha ^2} } \right)^2} + {g_2}\sum\nolimits_\alpha ^N {\varphi _\alpha ^4}$] We find strong indication for the stability of the cubic fixed point for the number of components N ≥ 3, implying that the magnetic transition of three-dimensional cubic crystals are described by critical exponents of the cubic universality class. Resummation procedures for theories with two coupling constants are still under investigation.