Abstract
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 ϕ4-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 β-functions of the renormalization group equation through the third order in the (4 ∈)-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.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 181, No. 2, pp. 374–386, November, 2014.
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Kalagov, G.A., Kompaniets, M.V. & Nalimov, M.Y. Renormalization-group study of a superconducting phase transition: Asymptotic behavior of higher expansion orders and results of three-loop calculations. Theor Math Phys 181, 1448–1458 (2014). https://doi.org/10.1007/s11232-014-0225-3
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DOI: https://doi.org/10.1007/s11232-014-0225-3