Critical behavior of the~$O(n)$ $\phi^4$ model with an~antisymmetric tensor order parameter: Three-loop approximation
Teoretičeskaâ i matematičeskaâ fizika, Tome 190 (2017) no. 2, pp. 239-253
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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.
@article{TMF_2017_190_2_a2,
author = {N. V. Antonov and M. V. Kompaniets and N. M. Lebedev},
title = {Critical behavior of the~$O(n)$ $\phi^4$ model with an~antisymmetric tensor order parameter: {Three-loop} approximation},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {239--253},
publisher = {mathdoc},
volume = {190},
number = {2},
year = {2017},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2017_190_2_a2/}
}
TY - JOUR AU - N. V. Antonov AU - M. V. Kompaniets AU - N. M. Lebedev TI - Critical behavior of the~$O(n)$ $\phi^4$ model with an~antisymmetric tensor order parameter: Three-loop approximation JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2017 SP - 239 EP - 253 VL - 190 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2017_190_2_a2/ LA - ru ID - TMF_2017_190_2_a2 ER -
%0 Journal Article %A N. V. Antonov %A M. V. Kompaniets %A N. M. Lebedev %T Critical behavior of the~$O(n)$ $\phi^4$ model with an~antisymmetric tensor order parameter: Three-loop approximation %J Teoretičeskaâ i matematičeskaâ fizika %D 2017 %P 239-253 %V 190 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_2017_190_2_a2/ %G ru %F TMF_2017_190_2_a2
N. V. Antonov; M. V. Kompaniets; N. M. Lebedev. Critical behavior of the~$O(n)$ $\phi^4$ model with an~antisymmetric tensor order parameter: Three-loop approximation. Teoretičeskaâ i matematičeskaâ fizika, Tome 190 (2017) no. 2, pp. 239-253. http://geodesic.mathdoc.fr/item/TMF_2017_190_2_a2/