Thermodynamic Gross-Neveu model under constant electromagnetic field

Abstract

Analyzed is the effective potential of D-dimensional thermodynamic Gross-Neveu model (defined by large-N leading order, $2\le D<4$) under constant electromagnetic field ($\vec{E}\cdot \vec{B}=0$). The potential is derived from a thermal analogy of the worldline formalism. In the magnetic case, the potential is expressed in terms of a discretized momentum sum instead of a continuum momentum integral, and it reproduces known critical values of $\mu$ and $T$ in the continuum limit. In the electric case, chiral symmetry is restored at finite $T$ (with arbitrary $\mu$) against instability of fermion vacuum. An electromagnetic duality is pointed out as well. Phase diagrams are obtained in both cases.

35 pages, latex with 11 figures

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• Magnetic polarizabilities of light mesons in $SU(3)$ lattice gauge theory
• Color neutral 2SC phase of cold and dense quark matter in the presence of constant magnetic fields
• Universality and the magnetic catalysis of chiral symmetry breaking
• $\rho$ mesons in strong abelian magnetic field in SU(3) lattice gauge theory
• The quark-hadron thermodynamics in magnetic field
• Improved ring potential of QED at finite temperature and in the presence of weak and strong magnetic field
• Temperature induced phase transitions in four fermion models in curved space-time
• Finite Density Effect in the Gross-Neveu Model in a Weakly Curved $R^1\times S^2$ Spacetime
• Dense Quark-Gluon Plasma in strong magnetic fields
• Integral representations of thermodynamic 1PI Green functions in the world-line formalism
• Neutral $\rho$ and $A$ mesons in magnetic field in SU(2) lattice gauge theory
• Chiral MHD description of a perfect magnetized QGP using the effective NJL model in a strong magnetic field
• Note on thermodynamic fermion loop under constant magnetic field