Four-fermion interactions and the chiral symmetry breaking in an external magnetic field

Abstract

We investigate the chiral symmetry and its spontaneous breaking at finite temperature and in an external magnetic field with four-fermion interactions of different channels. Quantum and thermal fluctuations are included within the functional renormalization group approach, and properties of the set of flow equations for different couplings, such as its fixed points, are discussed. It is found that external parameters, e.g. the temperature and the external magnetic field and so on, do not change the structure of the renormalization group flows for the couplings. The flow strength is found to be significantly dependent on the route and direction in the plane of couplings of different channels. Therefore, the critical temperature for the chiral phase transition shows a pronounced dependence on the direction as well. Given fixed initial ultraviolet couplings, the critical temperature increases with the increasing magnetic field, viz., the magnetic catalysis is observed with initial couplings fixed.

8 pages, 4 figures

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Cited by in corpus (6)

• QCD at finite temperature and density within the fRG approach: An overview
• Thermodynamics of 2+1 Flavor Polyakov-Loop Quark-Meson Model under External Magnetic Field
• Magnetic catalysis and diamagnetism from pion fluctuations
• Functional renormalization group study of neutral and charged pion under magnetic fields in the quark-meson model
• Spectral function for pions in magnetic field
• Quark condensate and magnetic moment in a strong magnetic field