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

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

1996-11-27

arxiv.org/abs/quant-ph/9611050v1

Phys.Rev. B56 (1997) 14428

Physics

Quantum Physics

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

Scientific paper

10.1103/PhysRevB.56.14428

For an anisotropic euclidean $\phi^4$-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 expansions in $d=4-\varepsilon$ dimensions, using the knowledge of the large-order behavior and Borel transformations. For $\varepsilon=1$, an infrared stable cubic fixed point for $M \geq 3$ 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.

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