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

Understand

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 $r\geq 4$ 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.