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

Abstract

The structure of the renormalization-group flows in a model with three quartic coupling constants is studied within the $\epsilon$-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 $\sqrt{\epsilon }$ to appear in the series is investigated. Reliability and effectiveness of the $\epsilon$-expansion method for the given model is discussed.

14 pages, LaTeX, no figures. To be published in Phys. Rev. B, V.57 (1998)

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