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The complete analysis of a model with three quartic coupling constantsassociated with an O(2N)--symmetric, a cubic, and a tetragonal interactions iscarried out within the three-loop approximation of the renormalization-group(RG) approach in $D=4-2\epsilon$ dimensions. Perturbation expansions for RGfunctions are calculated using dimensional regularization and the minimalsubtraction (MS) scheme. It is shown that for $N\ge 2$ the model does possess astable fixed point in three dimensional space of coupling constants, inaccordance with predictions made earlier on the base of the lower-orderapproximations. Numerical estimate for critical (marginal) value of the orderparameter dimensionality $N_c$ is given using Pad\'e-Borel summation of thecorresponding $\epsilon$--expansion series obtained. It is observed thattwo-fold degeneracy of the eigenvalue exponents in the one-loop approximationfor the unique stable fixed point leads to the substantial decrease of theaccuracy expected within three loops and may cause powers of $\sqrt{\epsilon}$to appear in the expansions. The critical exponents $\gamma$ and $\eta$ arecalculated for all fixed points up to $\epsilon^3$ and $\epsilon^4$,respectively, and processed by the Borel summation method modified with aconformal mapping. For the unique stable fixed point the magneticsusceptibility exponent $\gamma$ for N=2 is found to differ in third order in$\epsilon$ from that of an O(4)--symmetric point. Qualitative comparison of theresults given by $\epsilon$--expansion, three-dimensional RG analysis,non-perturbative RG arguments, and experimental data is performed.Comment: 30 pages, LaTeX, no figures. To be published in Phys. Rev. B, V.57,  Jan. issue (1998

physical review. b, condensed matter

Three-loop renormalization-group analysis of a complex model with stable fixed point: Critical exponents up to<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>ε</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>ε</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:…

Three-loop renormalization-group analysis of a complex model with stable fixed point: Critical exponents up toε3andε4