Large-Order Behavior of Two-coupling Constant $ϕ^4$-Theory with Cubic Anisotropy

Abstract

For the anisotropic $[u (\sum_{i=1^N ϕ_i^2)^2+v \sum_{i=1^N ϕ_i^4]$-theory with {$N=2,3$} we calculate the imaginary parts of the renormalization-group functions in the form of a series expansion in $v$, i.e., around the isotropic case. Dimensional regularization is used to evaluate the fluctuation determinants for the isotropic instanton near the space dimension 4. The vertex functions in the presence of instantons are renormalized with the help of a nonperturbative procedure introduced for the simple $g{ϕ^4$-theory by McKane et al.