Application of Thermal Renormalization Group method to fermionic models

Abstract

This thesis investigates the phase structure and critical behavior of fermionic models, specifically the Four-Fermion and Nambu-Jona-Lasinio models, using the Functional Renormalization Group (FRG) method. To address the challenge of losing non-trivial fixed points in finite-temperature systems, a modified thermal RG method is employed. It links the dimensionful temperature to the running momentum scale via a constant dimensionless temperature parameter. This approach recovers non-trivial points and demonstrates that the symmetric quark-gluon plasma phase expands as temperature increases and suppresses the broken phase of hadrons. Furthermore, the thesis shows that thermal effects shift the annihilation point of fixed UV and IR points of the scalar coupling in the gauged NJL model toward higher coupling values.