Stability of 3-D cubic fixed point in two coupling constant phi**4 theory

Nov, 1996
22 pages
Published in:
  • Phys.Rev.B 56 (1997) 14428
e-Print:

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1997200320092015202101234
Abstract:
For an anisotropic euclidean ϕ 4\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.
  • field theory: scalar
  • dimension: 3
  • renormalization group: transformation
  • renormalization group: beta function
  • perturbation theory: higher-order
  • energy: ground state
  • numerical calculations