This article is cited in 11 papers

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

N. V. Antonov, M. V. Kompaniets, N. M. Lebedev

Saint Petersburg State University, St. Petersburg, Russia

Abstract: We consider the critical behavior of the $O(n)$-symmetric model of the $\phi^4$ 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.

Keywords: critical behavior, tensor order parameter, renormalization group.

Received: 23.12.2015
Revised: 27.01.2016

DOI: 10.4213/tmf9130

 English version: Theoretical and Mathematical Physics, 2017, 190:2, 204–216

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