Renormalization-group investigation of a superconducting $U(r)$-phase transition using five loops calculations

Abstract

We have studied a Fermi system with attractive $U(r)$-symmetric interaction at the finite temperatures by the quantum field renormalization group (RG) method. The RG functions have been calculated in the framework of dimensional regularization and minimal subtraction scheme up to five loops. It has been found that for $r\ge 4$ the RG flux leaves the system's stability region -- the system undergoes a first order phase transition. To estimate the temperature of the transition to superconducting or superfluid phase the RG analysis for composite operators has been performed using three-loops approximation. As the result this analysis shows that for $3D$ systems estimated phase transition temperature is higher then well known theoretical estimations based on continuous phase transition formalism.

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Cited by in corpus (8)

• Minimally subtracted six loop renormalization of $O(n)$-symmetric ${\varphi }^4$ theory and critical exponents
• Six-loop $\epsilon$ expansion study of three-dimensional $n$-vector model with cubic anisotropy
• Six-loop beta functions in general scalar theory
• Six-loop $\epsilon$ expansion study of three-dimensional $O(n)\times O(m)$ spin models
• Six-loop $\epsilon$ expansion of three-dimensional $\text{U}(n)\times \text{U}(m)$ models
• Universal effective couplings of the three-dimensional $n$-vector model and field theory
• Superfluidity in multicomponent fermions via the functional renormalization group
• Fluctuation-induced first-order superfluid transition in unitary $\mathrm{SU}(N)$ Fermi gases