Thermodynamics of the Massive Gross-Neveu Model

Abstract

We study the thermodynamics of massive Gross-Neveu models with explicitly broken discrete or continuous chiral symmetries for finite temperature and fermion densities. The large $N$ limit is discussed bearing attention to the no-go theorems for symmetry breaking in two dimensions which apply to the massless cases. The main purpose of the study is to serve as analytical orientation for the more complex problem of chiral transition in $4-$dimensional QCD with quarks. For any non-vanishing fermion mass we find, at finite densities, lines of first order phase transitions. For small mass values traces of would-be second order transitions and a tricritical point are recognizable. We study the thermodynamics of these models, and in the model with broken continuous chiral symmetry we examine the properties of the pion like state.

34 pages (+18 figures, available upon request to [email protected]), LATEX file, uses art12a.sty, macro included, UGVA-DPT 1994/06-854

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• Inhomogeneous charged pion condensation in chiral asymmetric dense quark matter in the framework of NJL${}_2$ model
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• Critical and Tricritical Points for the Massless 2d Gross-Neveu Model Beyond Large N
• Finite-size effects in pion condensation phenomena of dense baryonic matter in the NJL${}_2$ model
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• Tricritical behavior of the massive chiral Gross-Neveu model
• Properties of the massive Gross-Neveu model with nonzero baryon and isospin chemical potentials
• Charged pion condensation and duality in dense and hot chirally and isospin asymmetric quark matter in the framework of NJL${}_2$ model
• Pion condensation in the Gross-Neveu model with nonzero baryon and isospin chemical potentials
• From non-degenerate conducting polymers to dense matter in the massive Gross-Neveu model
• No First-Order Phase Transition in the Gross-Neveu Model?
• Cooper pairing and finite-size effects in a NJL-type four-fermion model
• Phase structure of the 1+1 dimensional Nambu--Jona-Lasinio model with isospin
• Duality between chiral symmetry breaking and charged pion condensation at large $N_c$: Consideration of an NJL${}_2$ model with baryon-, isospin- and chiral isospin chemical potentials
• Charged pion condensation in dense quark matter: Nambu--Jona-Lasinio model study
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• Phase transition in the massive Gross-Neveu model in toroidal topologies
• Superconducting phase transitions induced by chemical potential in (2+1)-dimensional four-fermion quantum field theory
• The Gross-Neveu model at finite temperature at next to leading order in the 1/N expansion
• Phase transition in the 3-D massive Gross-Neveu model
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• Dulaity and charged pion condensation in chirally asymmetric dense quark matter in the framework of an NJL${}_2$ model
• Inhomogeneous chiral phase in the magnetic field
• The Gross-Neveu model on a sphere with a magnetic monopole
• Critical and tricritical exponents of the Gross-Neveu model in the large-$N_f$ limit
• Beth-Uhlenbeck equation for the thermodynamics of fluctuations in a generalised 2+1D Gross-Neveu model
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