Аннотация: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.