# Six-loop $\varepsilon$ expansion study of three-dimensional $n$-vector model with cubic anisotropy

## TL;DR

This paper performs a six-loop epsilon expansion analysis of the three-dimensional n-vector model with cubic anisotropy, providing refined estimates of critical properties and confirming the stability of the cubic fixed point for n=3.

## Contribution

The study extends previous analyses by calculating six-loop expansions and applying resummation techniques to improve estimates of critical exponents and fixed point stability.

## Key findings

- Cubic fixed point is stable for n=3.
- Refined critical exponents for the cubic universality class.
- Comparison with previous theoretical and lattice results.

## Abstract

The six-loop expansions of the renormalization-group functions of $\varphi^4$ $n$-vector model with cubic anisotropy are calculated within the minimal subtraction (MS) scheme in $4 - \varepsilon$ dimensions. The $\varepsilon$ expansions for the cubic fixed point coordinates, critical exponents corresponding to the cubic universality class and marginal order parameter dimensionality $n_c$ separating different regimes of critical behavior are presented. Since the $\varepsilon$ expansions are divergent numerical estimates of the quantities of interest are obtained employing proper resummation techniques. The numbers found are compared with their counterparts obtained earlier within various field-theoretical approaches and by lattice calculations. In particular, our analysis of $n_c$ strengthens the existing arguments in favor of stability of the cubic fixed point in the physical case $n = 3$.