Stability of 3D Cubic Fixed Point in Two-Coupling-Constant ϕ^4-Theory

Abstract

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

Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html . Paper also at http://www.physik.fu-berlin.de/~kleinert/kleiner_re250/preprint.html