On stability of the three-dimensional fixed point in a model with three coupling constants from the $ε$ expansion: Three-loop results

Abstract

The structure of the renormalization-group flows in a model with three quartic coupling constants is studied within the $ε$-expansion method up to three-loop order. Twofold degeneracy of the eigenvalue exponents for the three-dimensionally stable fixed point is observed and the possibility for powers in $\sqrtε$ to appear in the series is investigated. Reliability and effectiveness of the $ε$-expansion method for the given model is discussed.