Theoretical and Mathematical Physics

, Volume 190, Issue 2, pp 204–216 | Cite as

Critical behavior of the O(n) ϕ 4 model with an antisymmetric tensor order parameter: Three-loop approximation

  • N. V. AntonovEmail author
  • M. V. Kompaniets
  • N. M. Lebedev


We consider the critical behavior of the O(n)-symmetric model of the ϕ 4 type with an antisymmetric tensor order parameter. According to a previous study of the one-loop approximation in the quantum field theory renormalization group, there is an IR-attractive fixed point in the model, and IR scaling with universal indices hence applies. Using a more specific analysis based on three-loop calculations of the renormalization-group functions and Borel conformal summation, we show that the IR behavior is in fact governed by another fixed point of the renormalization-group equations and the model therefore belongs to a different universality class than the one suggested by the simplest one-loop approximation. Nevertheless, the validity of the obtained results remains a subject for discussion.


critical behavior tensor order parameter renormalization group 


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Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  • N. V. Antonov
    • 1
    Email author
  • M. V. Kompaniets
    • 1
  • N. M. Lebedev
    • 1
  1. 1.Physics FacultySt. Petersburg State UniversitySt. PetersburgRussia

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