Finite-size effects in the Gross-Neveu model with allowance for isospin and baryon chemical potentials

The properties of the (1 + 1)-dimensional massless Gross-Neveu model were studied for a compactified space S ¹, as well as with allowance for nonzero values of the baryon (µ) and isospin (µ _I ) chemical potentials. Our investigation was performed in the limit of a large number of fermion colors, N _c . It is shown that, for L→∞(case of an unbounded volume), the pion-condensation phase characterized by zero quark density is formed at any nonzero value of µ _I and a small value of µ. For any finite value of L (case of a bounded volume), the phase portrait of the model contains a pion-condensation phase where the quark density is nonzero. Thus, finite dimensions of the system being considered may serve as a factor that facilitates the formation of a pion-condensation phase in quark matter with a nonzero baryon density. At the same time, the phase where chiral symmetry is broken may exist only at very large values of L.