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

TL;DR

This paper uses five-loop renormalization group calculations to analyze a Fermi system with attractive $U(r)$ interaction, revealing a first-order phase transition for $r extgreater=4$ and estimating transition temperatures higher than previous models.

Contribution

It provides a detailed five-loop RG analysis of $U(r)$-symmetric interactions and identifies the nature of phase transitions in such systems, extending prior lower-loop studies.

Findings

First-order phase transition for $r extgreater=4$

RG flux leaves stability region at high $r$

Estimated transition temperature exceeds previous theoretical predictions

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 $r\geq 4$ 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. 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.