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Stability of a three-dimensional cubic fixed point in the two-coupling-constant<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>φ</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>theory
For an anisotropic Euclidean ${\ensuremath{\varphi}}^{4}$ theory with two interactions $[u({\ensuremath{\sum}}_{i=1}^{M}{\ensuremath{\varphi}}_{i}^{2}{)}^{2}+v{\ensuremath{\sum}}_{i=1}^{M}{\ensuremath{\varphi}}_{i}^{4}]$ the $\ensuremath{\beta}$ functions are calculated from five-loop perturbation expansions in $d=4\ensuremath{-}\ensuremath{\varepsilon}$ dimensions, using the knowledge of the large-order behavior and Borel transformations. For $\ensuremath{\varepsilon}=1$, an infrared-stable cubic fixed point for $M>~3$ is found, implying that the critical exponents in the …