Renormalization-group study of a~superconducting phase transition: Asymptotic behavior of higher expansion orders and results of three-loop calculations
Teoretičeskaâ i matematičeskaâ fizika, Tome 181 (2014) no. 2, pp. 374-386
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We use quantum-field renormalization group methods to study the phase transition in an equilibrium system of nonrelativistic Fermi particles with the ‘`density–density" interaction in the formalism of temperature Green’s functions. We especially attend to the case of particles with spins greater than $1/2$ or fermionic fields with additional indices for some reason. In the vicinity of the phase transition point, we reduce this model to a $\phi^4$-type theory with a matrix complex skew-symmetric field. We define a family of instantons of this model and investigate the asymptotic behavior of quantum field expansions in this model. We calculate the $\beta$-functions of the renormalization group equation through the third order in the $(4{-}\epsilon)$-scheme. In the physical space dimensions $D=2,3$, we resum solutions of the renormalization group equation on trajectories of invariant charges. Our results confirm the previously proposed suggestion that in the system under consideration, there is a first-order phase transition into a superconducting state that occurs at a higher temperature than the classical theory predicts.
Keywords:
temperature Green's function, superconductivity, renormalization group, instanton analysis, Borel summation.
@article{TMF_2014_181_2_a9,
author = {G. A. Kalagov and M. Yu. Nalimov and M. V. Kompaniets},
title = {Renormalization-group study of a~superconducting phase transition: {Asymptotic} behavior of higher expansion orders and results of three-loop calculations},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {374--386},
publisher = {mathdoc},
volume = {181},
number = {2},
year = {2014},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2014_181_2_a9/}
}
TY - JOUR AU - G. A. Kalagov AU - M. Yu. Nalimov AU - M. V. Kompaniets TI - Renormalization-group study of a~superconducting phase transition: Asymptotic behavior of higher expansion orders and results of three-loop calculations JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2014 SP - 374 EP - 386 VL - 181 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2014_181_2_a9/ LA - ru ID - TMF_2014_181_2_a9 ER -
%0 Journal Article %A G. A. Kalagov %A M. Yu. Nalimov %A M. V. Kompaniets %T Renormalization-group study of a~superconducting phase transition: Asymptotic behavior of higher expansion orders and results of three-loop calculations %J Teoretičeskaâ i matematičeskaâ fizika %D 2014 %P 374-386 %V 181 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_2014_181_2_a9/ %G ru %F TMF_2014_181_2_a9
G. A. Kalagov; M. Yu. Nalimov; M. V. Kompaniets. Renormalization-group study of a~superconducting phase transition: Asymptotic behavior of higher expansion orders and results of three-loop calculations. Teoretičeskaâ i matematičeskaâ fizika, Tome 181 (2014) no. 2, pp. 374-386. http://geodesic.mathdoc.fr/item/TMF_2014_181_2_a9/