Stability of a three-dimensional cubic fixed point in two-coupling-constant phi^4-Theory

For an anisotropic euclidean phi^4 field theory with two interactions$[u (\sum_{i=1}^M {\phi}_i^2)^2+v \sum_{i=1}^M \phi_i^4]$the $\beta$-functions are calculated from five-loop perturbation expansionsin $d=4-\varepsilon$ dimensions,using the knowledge of the large-order behavior and Borel transformations.For $\varepsilon=1$, an infrared stable cubicfixed point for $M \geq 3$ is found,implying that the critical exponents in the magnetic phase transitionof real crystals are of the cubic universality class.There were previous indications of the stability based either onlower-loop expansions or on less reliable Pad\'{e} approximations,but only the evidence presented in this work seems to besufficently convincing to draw this conclusion.