Stability of 3-D cubic fixed point in two coupling constant phi**4 theory
Nov, 1996Citations per year
Abstract:
For an anisotropic euclidean -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.Note:
- 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
- field theory: scalar
- dimension: 3
- renormalization group: transformation
- renormalization group: beta function
- perturbation theory: higher-order
- energy: ground state
- numerical calculations
References(17)
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