Properties of the massive Gross-Neveu model with nonzero baryon and isospin chemical potentials

Abstract

The properties of the two-flavored Gross-Neveu model with nonzero current quark mass are investigated in the (1 þ 1)-dimensional space-time at finite isospin I as well as quark number chemical potentials and zero temperature. The consideration is performed in the limit N c ! 1, i.e., in the case with an infinite number of colored quarks. In the plane of parameters I , a rather rich phase structure is found, which contains phases with and without pion condensation. We have found a great variety of onequark excitations of these phases, including gapless and gapped quasiparticles. Moreover, the mesonic mass spectrum in each phase is also investigated.

CHARGED PION CONDENSATION PHENOMENON OF DENSE BARYONIC MATTER INDUCED BY FINITE VOLUME: THE NJL2 MODEL CONSIDERATION

“…In particular, it turns out that the PCd phase is forbidden in the framework of the NJL-type models if bare quark masses reach the physically acceptable values of 5 ÷ 10 MeV (see [13]). In addition, recent investigations of the charged pion condensation phenomenon in terms of the (1+1)-dimensional massive/massless NJL 2 model in R 1 × R 1 spacetime shows that the PCd phase is also absent there [32] (see also Sec. III A of the present paper).…”

“…It is clear that the TDP (15) is an ultraviolet divergent quantity, so one should renormalize it, using a special dependence of the bare quantities, such as the bare coupling constant G ≡ G(Λ), on the cutoff parameter Λ (Λ restricts the integration region in the divergent integrals, |p 1 | < Λ). The detailed discussion of this procedure was performed, for example, in papers [31,32]. The main stages of it are the following.…”

“…This follows from the fact that in the limit of large N c the quantum fluctuations, which would otherwise destroy a long-range order corresponding to a spontaneous symmetry breaking, are suppressed by 1/N c factors. Thus, the effects inherent for real dense quark matter, such as color superconductivity (spontaneous breaking of the continuous color symmetry) or charged pion condensation (spontaneous breaking of the continuous isospin symmetry) might be simulated in terms of a simpler (1+1)-dimensional GN-type model, though only in the leading order of the large N c approximation (see, e.g., [26,30] and [31,32], respectively). Finally, one should recall that both the chiral phase transition [33] and color superconductivity [30] were investigated in the framework of GN models with account of the nontrivial R 1 × S 1 spacetime topology.…”

Deconfinement transition at high isospin chemical potential and low temperature

“…But we can ignore the electromagnetic and weak effects in order to isolate the strong dynamics [2]. There have been considerable recent developments in this region of the phase diagram [1,2,[28][29][30][31][32][33][34].…”

Spontaneous parity violation under extreme conditions: an effective lagrangian analysis

“…Although the issue of SPB in hadronic phase has been touched upon in the pion-nucleon theory [1,[40][41][42]55] and in NJL models [56][57][58][59][60], the reliability of the models used is not quite clear for intermediate nuclear densities. The reason is discussed in the next section: they are not rich enough to explore the subtle phenomenology involved.…”