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

TL;DR

This paper investigates the large-order behavior of two-coupling $ ext{phi}^4$-theory with cubic anisotropy, focusing on the imaginary parts of RG functions near the isotropic case using instanton calculus and nonperturbative renormalization.

Contribution

It introduces a nonperturbative method to evaluate the imaginary parts of RG functions in anisotropic $ ext{phi}^4$-theory, extending instanton analysis to theories with multiple couplings.

Findings

Calculated imaginary parts of RG functions as series in $v$

Applied dimensional regularization to evaluate fluctuation determinants

Renormalized vertex functions using a nonperturbative approach

Abstract

For the anisotropic $[u (\sum_{i=1^N {\phi}_i^2)^2+v \sum_{i=1^N \phi_i^4]$-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 $g{\phi^4$-theory by McKane et al.